Foals get the parents PS ÷2. So if your foal has about half the PS of the parents that is correct.

PS is kinda unimportant when it comes to breeding. Your foal's potential is limited by its training boost (TB) which is the parents levels ÷10.

A foal with 1TB will get only +1PS per training (on top of the rng based stats it gains) where's a 10TB horse will get +10PS per training. Personally I don't breed my horses until they're around level 80 so my foals get at least 16TB.

So basically, the amount of PS a horse can gain over its lifetime is limited by its TB. 

Of course you want higher TB and it limits your PS but I wouldn't say PS isn't important, especially for discipline horses. Its how you enter higher tiered shows. 

You do want to make sure you breed with a minimum level 50 parents so foals can have at least 10 TB so not limiting PS but beyond that aspect, yes foals do get half their parents PS and then with higher TB and training, the PS will raise.