Agree with Dave regarding technology, but this is no reason not to do something though, if it was, you'd never put anything into service for fears it'd be overtaken by the time you did. The concept worked very well in the Mosquito, and even once the Germans introduced jet fighters to intercept it, the Mossie was an effective aircraft in the jobs that it carried out. The Ar 234 was unstoppable over the UK because of its speed and altitude and was a formidable weapon, just because the Allies might have produced something to counter it eventually would be a silly reason for the Germans not to attempt to put it into service. The short period of time might be enough to force a change in long term strategy - obviously depending on a given situation, but if you are not going to try, why bother playing?
Nah, the 234 real use was for photo-recon. Sure it was fast, but it all comes back to bombing accuracy and the correct targets. Say, in some wonderful wishland they had 1,000 of them in say late 43 (totally impossible of course, but this is a thought experiment) What could they do? There has been no photo recon for 3 years over the UK, so they don't know what to hit any better than they knew in the BoB. Light bomb load therefore they have to get down low to achieve bombing accuracy where they are as vulnerable as anything else to flak. They would have just lost lots, while the allies had the option of hammering their airfields at will (either through tactical or strategic bombers) further hampering them.
Funnily enough their V1 campaign was more rational (the V2 was a joke). The V1 was cheap to develop and build so they could throw thousands at the UK, Antwerp, etc. It cost the allies far more in resources to defend against them that it cost the Germans to use them, so it was a sort of strategic win for them. Unfortunately the V1 was so inaccurate and thanks to great counter intelligence (read R.V Jones book) they were mislead so that it became even more inaccurate. Their lack of photo recon meant they had no idea what was being hit by any objective measures.
The dominance of Allied photo recon is always underestimated by most commentators. Both at the tactical and strategic levels. High altitude PR Spits and Mossies along with low level Spits and Mustangs (the 'Dicers') dominated the battlefields and airspace throughout the Continent for years. The Germans usually had no idea what was happening, they knew nothing about the D-Day build up for example, while their counterparts (well those who used it properly) had very clear ideas of what they were facing.
Again the Germans had nothing with the performance of the high alt PR Spits and Mossies, they went everywhere with impunity. The low level boys had a rougher time of course because of flak, but the low level PR Spits and Mustangs were still way above the performance levels of their opposition.
Trouble was the prop airframes the Germans had could be matched quite easily. Yes the 109 could (and were) used for high alt PR, but they didn't have the performance advantage that stopped them from being shot down. The 190 had the same issue, yes it was good at low altitude but not good enough to survive against the defences the UK had. And none had any real range.
Again back to RV Jones as an example, he had mapped all the German Channel radar network, so before and during D-Day it was easily destroyed and spoofed.
So the only useful contribution the 234 could have made was as a PR plane, no matter how many they had. Good contribution no less though. With that sort of info in June 44 Rommel might have been able to persuade Hitler to give him the forces to kill the invasion in Normandy... maybe (he only had about 3-7 days to do it, after that it was only a matter of time). Poor old Rommel, wonder boy until Monty thumped him .. again and again and again.....