I have never seen a zero turn that doesn't have levers to disengage so you can push the mower in neutral.
Then you haven't worked on enough of them then. Currently I have a JD 652R which has the same pump style system as the OPs mower. I also have a JD 830A in the shop with Parker pumps that uses the same style release system where you need a wrench to enter bypass mode.
And I remember correctly the two Hustler Super Zs I work on uses the Hydro Gear pumps too. Along these are the Scag Turf Tigers that I service.
Many of the customer grade ZTRs are integrated transaxles which do use levers to disengage the hydro and several commercial units are now using these integrated units. Both the Z925A is a royal pain to R&R one of the units as both along mounting plate has to be removed in order to separate a hydro for service or replacement. So glad the Z950 was improved on how the hydros were mounted. Still a pain but at least you can remove just the one that needs servicing.