Hydrangea macrophylla flowers on old wood. That is the flowers will form on growth from this year, next year. Flowers this year would have been on growth from the previous year. So if you remove that wood then you are removing potential flowers which is possibly why you only get a few blooms.
In late Spring I would very carefully remove the spent blooms without removing any of the growth underneath them.
Under normal growing conditions they need very little pruning until they are getting old when remedial removal of about a third of the growth may be needed to encourage new branches from low down on the shrub.
Try giving them a good feed as well.

I agree, it sounds as if you are removing the dormant flowers when you do your tidy up. Do as Owd says and just take the dead flower heads off, follow the dead stalk down to where the new buds are and snip the stalk off there.

Agree, the reason you don't see any blooms is that you keep cutting them off. Yes, sometimes you'll get a few meager flowers on new growth, but the big showy ones you want bloom on old wood. The best time to prune is early summer. They start setting their buds in the summer for the following spring.

I know it's a matter of preference, but I never cut off the old blooms. They eventually fade to red, then brown. I think it's a beautiful autumn display. I do the 'tidy up' early spring just before it breaks bud removing only dead debris.

'Old fashioned mophead hydrangeas bloom on old wood and are pruned in the same way as the lacecap hydrangeas. Each year you should remove one third of the oldest branches and prune the remainder back slightly after flowering if you want to keep the shrub's size in check.'

https://www.thespruce.com/identifying-old-fashioned-hydrangea-1402687