The USN actually called for Merlin engined fighters for both shore and carrier operations:
I suspect that the USN might have welcomed the Sea Hurricane in 1942.
One Admiral, Adm. Frank Jack Fletcher called for 'P-40F or other suitable aircraft' to be considered for carrier suitability. Considering Fletcher's reputation among senior USN aviation leadership that is a suggestion that is unlikely to be given serious consideration, whatever one thinks of Fletcher, one admiral (and a black shoe admiral at that) is hardly "the USN". In fact, it's quite possible that Fletcher's endorsement of such a proposal if anyone else supported it, killed it outright.
However, I doubt they would have given the notion more than a passing thought and certainly not 'welcomed' any such infusion of such airframes… for a number of reasons some of which have already been noted here.
The FAA didn't resist single seat fighters and used them throughout the war. However, they needed a folding wing fighter that could fit into the narrow lifts on Ark Royal and the Illustrious class carriers and there were no such single seat fighters in service in the RN or USN until late 1941, however by mid 1941 the Sea Hurricane was being used on FAA carriers with larger lifts and in 1942 even on the Illustrious class via a temporary deck park.
The ideal use for the Sea Hurricane would have been as a point defence fighter in lieu of the Wildcats that were kept as CAP (rather than escorts) where it's high climb rate would have allowed it to gain the altitude advantage over incoming raids and provide top cover for the Wildcat, while the Sea Hurricane I would have given USN pilots speed parity with the zero under 10k ft along with better overall manoeuvrability. The Sea Hurricane II could carry twin 45IG drop tanks and could have served as an escort fighter but without folding wings it could not be carried in the same numbers as the F4F-4.
We'll just have to agree to disagree about the FAA or RN's '
resistance' to single seat fighters. In my view, if a navy dedicates its limited resources toward the development of two-seat dive bomber-fighters or fighter-recon aircraft (whatever its justification) and then decides it must procure single seat fighter aircraft from other sources… its demonstrated a certain resistance or reluctance by how it prioritizes its expenditures of money.
Just to clarify, time line for the F4F-3 (whose interceptor climb performance is competitive with that of the HSH): Initial sea trials of the F4F were in Early December. 1940. 22 F4F-3 were produced in late 1940 while an additional 27 were delivered to the USN by February 21, 1941 with 19 more by July 2, 1941. That's 68 F4F-3's sufficient to equip more than three squadrons by midyear.
Squadron transitions to the F4F-3 began in November 1940. By Late 1941, Half the USN carrier air wings (except VF-5, 6 and 2) were equipped with F4F-3s. VF-2 was equipped with F2A-3 (Transition from F2A-2 August, 1941) while the VF-5 6 transitioned to F4F-3As on or about in May 1941 (an investment made in their future receipt of F4F-3s or as it turned out, the F4F-4.)
Otherwise transitions to F4F-3 occurred as follows with Atlantic Fleet Carriers having first dibbs on the new A/C:
VF-41: November, 1940.
VF-72: January 1940
VF-42: March, 1941
VF-71: March, 1941
VF-3: August, 1941.
By the end of 1941 Grumman had completed its initial run of 185 F4F-3s and was already producing the F4F-4 variant. Apparently by December 31, 1941 all USN Carrier groups were equipped with F4F-3s except for VF-2 (F2A-3) and 6 (F4F-3A) although some of these were understrength (Sara's e.g. VF-3), some were also overstrength.
AFAIK, only 5 F4F-4 were produced for the USN in 1941. But production accelerated quickly with squadron transitions beginning soon after the new year.
In contrast, (folding wing) Martlet II deliveries beginning on October 4, 1941 amounted to 48 A/C by December 31, 1941. Prior to that 91 Martlet I and II were delivered between July 27, 1940 and March 14, 1941. This just validates your statement about such folding wing single seat fighter aircraft did not becoming available until late '41.
Ignoring the previously mentioned significant logistical challenges of a fighter squadron with dissimilar type a/c, there are a variety of better options and good reasons why the addition of a fixed-wing Sea Hurricane or for that matter a navalized fixed-wing P-40F to USN carrier air wing in 1941-42 is a poor option.
If a mixed composition fighter squadron was desired, the addition of smaller F4F-3's, whose performance was not too dissimilar to that of the initial HSH (except in its max speed), would be a more logistically suitable option with aircrew already trained in type. In early 42, before there were sufficient numbers of F4F-4s became available, such mixed (F4F-3 F4F-4) air groups were not uncommon.
Also, the F4F made possible operational options that may have made it more attractive than one might expect despite its relatively poor performance.
Aside from its anemic climb rate, the biggest objection to the F4F-4 that many pilots expressed was in the reduced firing time of the -4 from the -3's 30+ seconds to 18 seconds; I believe that's about the same as a HSH with 8 .303 lmg. However, It looks like F4F equipped squadrons also had the option of removing two HMGs and reducing ammo supply which could reduce the weight by about 300 lbs. That would recover some of the lost performance of the original F4F-3 but of course further reduce firing time. Alternatively, the original max-load configuration could be retained accepting the performance degradation and the two outboard guns used to extend firing time albeit at a lower volume of fire. Whether any of these options was ever exercised is unknown. But the HSH or P-40F options were more limited with endurance that was already extended by the use of external tanks to be comparable with the F4F-3 or 4. AFAIK, from about May 1942 on, the range comparison bar was additionally raised by extending the Grumman's own range with disposable tanks.
It is clear that proper tactics allowed the F4F for all its faults to be an effective fighter and that whatever configuration was used in combat, it apparently got the job done.
In the final analysis, the fact that the F4F's small flight deck footprint allowed many more fighters to be carried significantly outweighs the lack of performance. It's true that most carrier vs carrier combat starts at no more than 20 or so thousand feet and progresses to lower altitudes. It's also true that the air battle over Guadalcanal, the turning point of the Pacific war, was largely waged at the higher altitudes where the F4F's two stage SC was an important factor.
The marines on Guadalcanal were always short of VF VMF F4F-4s. Their numbers were frequently replenished by the land-basing of USN fighter squadrons from the carriers sunk and damaged during the campaign. Attrition was so high that reducing the numbers of embarked USN VF could have compromised the ability of the marine defenders to protect themselves from aerial attack. The HSH's performance edge was not likely to be good enough to balance such losses.
Lt. General Ross E. Rowell Commander Marine Air Wings Pacific, said, " What saved Guadalcanal was the loss of so many carriers." In other words, it was shear numbers of F4F-4's that made the difference, not performance.