There's no type of house that is unsuitable, since an inefficient, badly insulated property will be so regardless of the heating source, although individual circumstances might prevent an ASHP.
But most talk is about wet systems where there are issues, particularly trying to adapt an existing installation. It might be worth looking into Air to air (A2A) where you could dip a toe in the water quite cheaply and simply from an installation point of view. Perhaps just start with your main living room as an experiment.
I hope to go A2A this summer, keeping gas for the first winter and then removing the rads and gas meter (and standing charge!) should the experiment go well. My 3 bedroom property is well insulated and I'll probably only go for a split with one emitter downstairs and one upstairs. The latter would be more more cooling in summer heatwaves, which is of course the other advantage of A2A.
I also have PV but no battery and this should certainly help during the shoulder months.