Interesting. I recently, a few months ago, replaced my 15 to 20 year old Craftsman mower like that with a new IKON X52 zero turn mower. And my Craftsman mower was a hydrostatic drive. And that mower still is working perfectly with the Kohler 15 HP engine. It now is living at my son's home and still working prefect.
I can say, one time I thought the hydro dive was going out because it got to where I couldn't barely drive up a slight slope with it anymore. So I bought another hydrostatic drive off Ebay for a song and replaced mine. It still wouldn't pull itself up a slight slope yet. So I decided to change the drive belt, like I should have done in the first place. And it took off like a rocket again. So my old hydro drive was still perfect. And I piece parted it out and earned a few dollars as well doing that.
So yes it could be slow if the drive belt isn't in good condition. And as far as the hydro drive goes, there are some out there as a replacement if need be and not very expensive. JMHO