Hmm, a little simplistic. In fact, the Mosquito was liked by the Americans and requested in increasing numbers throughout the war. You need to read the book Mosquito by C Martin Sharp and Mike Bowyer. There's a chapter on its US use and the decisions behind its acquisition by the USAAF. There is a sometime contributor (an American) to this forum who supplied information on the US use of the Mossie for the book - can't remember his handle. He's writing a book on the subject.
From the book: "A postgram from Washington, received by the Air Ministry on 23 February 1943, brought the first official request from the Americans for Mosquitoes. it read as follows: 'We desire to re-equip photo reconnaissance squadrons in, or destined for, the European theatre at 65 UE and North Africa at 26 UE with the PRU version of your Mosquito aircraft modified for American cameras. When we compare our aircraft in production anfd the tactical operational range of your Mosquito with our F-5/P-38, there seems no doubt the purposes of our combined air forces will be best served if the AAF curtail their conversion of P-38 and rely on your Mosquito production."
"There was a further aspect to America's wish to have Mosquitoes, for the US Navy had acquired a Canadian Mosquito and examined it from the night fighting aspect for which the USAAF and Navy had no suitable aircraft in prospect."
According to the book, Hap Arnold pressed the British Air Ministry on 1 April 1943 for Mosquitoes, but was met with resistance since the British themselves did not have enough, then on 14 April he again requested Mosquitoes, stating that it was of, "vital importance for the Allied Theatre Command for special mapping projects and that the Moquito can go far byond the F-5 range". A week late the US Navy stated it wanted 150 Mosquitoes from Canadian production."
The USAAF then submitted a request for the aircraft again, breaking down what they wanted in numbers. From the book: "A total of 235 were resquested for use by the end of 1943, by the 13th Photo Squadron in the 8th AF, the 5th and 13th Photo Squadron in the 12th AF, also the 22nd and 23rd Squadrons at Colorado Springs the 27th and one other training squadron. Each needed to be 13 aircraft strong with three reserves and others to cater for attrition."
"October 1943 saw the USAAF pressing for more PR Mosquitoes to equip two squadrons in the Mediterranean area and basing its requirement on 16 aircraft as each unit's strength with another 50 in reserve and 20 per month to cope with wastage."
"Their 1944 requirements would be 125 PR Mosquitoes, delivered at 76 per month from July onwards. If 30 FB.VIs still on offer were accepted they estimated a need for an additional one per month in 1944..."
"The value of the Mosquito as a strategic and target reconnaissance aircraft deeply impressed the USAAF which had nothing remotely comparable. In March 1944 Gen Arnold had filed a request for reconnaissance Mosquitoes for use in the Pacific war."
Doesn't sound to me like 'that was that' at all.