To me the felt under the keys is for comfort and noise reduction and in no way limits the response of the reeds or the playability of the box, quite the opposite in fact. The speed the reeds respond to the air flow is down to a combination of factors.

The gap between the reed and the plate. The smaller this gap the less air is required to move the reed so top quality hand made reeds will sound earlier (and clearer) than lower quality Tipo-a-mano or machine made reeds. (However the gap can be too small)

The size of the reed. The larger the reed the more air is required to move it especially the lowest 16' reeds but the better the quality box the less marked this is.

Overall condition of the box and build quality. Leaky bellows, gaskets, valves will all waste air and slow down the response of the reeds.

Basically, you can tell the quality of the box by the response of the reeds. If they all sound well, at consistent air pressures (both low and high), then you've got a good box