De Havilland actually did consider putting Griffons in the Mosquito. Before the prototype's design was finalised in 1940 there was a variant that was estimated on paper to be fitted with Griffons. Following on from the basic design, DH drew up two new designs based on the same airframe's manufacturing methods, the DH.101 powered by two Napier Sabres, again, one of the considered powerplants prior to finalisation of the prototype, and the DH.102 powered by Griffons. Both these aircraft were going to be slightly bigger but incorporating the basic layout of the Mossie.
The DH.102 was canned at the end of 1942 despite Air Staff interest because the company was overworked and had too many other commitments. Once it ended, the work force was instructed to proceed with the Hornet and Vampire, which represented better investments of time and energy, the latter considering it was a jet. The increase in performance and capability of the fitting of the 60 Series Merlins to the Mossie gave it an edge and this was a reason why other advanced twin engined aircraft by other companies - the Gloster Reaper, the Hawker P.1005 for example, were not proceded with, that and both firms had more urgent matters to be proceeding with.