At my flight school, we always set up the check ride. Our students are never responsible for that.
At the place I'm at now, it's cooperative. They expect adults to be able to call other adults and schedule things, but if the aircraft has a maintenance issue, or there's other circumstances, the instructors are there and available to assist.
You also don't get to call the examiner until the instructor says call and makes sure all endorsements are in the book and everything is ready.
It's kinda a "life PIC" thing. If you can't handle making some phone calls and scheduling stuff... which really shouldn't be any big deal.
Circumstance might dictate the instructor being involved from the start though, like the last couple of years where the FSDO has been unusually slow in scheduling initial CFI rides. The instructors around here seem to be quite involved in that process, since it helps move things along.
Just be glad you didn't get caught up in the 1 August 2016 ATP-MEL fiasco (itself a byproduct of the 1 August 2014 old ATP written sunset deadline), and the straight up highway robbery, pay-2-play scheme that was going on, in cash, all over the Country as a result of the timing glut. Plenty of people had to retake their checkrides after the cash was gone, as their DPEs got busted in short order. The only losers were the applicants out ~700 dollars (what I paid for my checkride) plus whatever they incurred getting recurrent in the airplane to replicate another checkride. Talk about double jeopardy.
Ditto the comments about the old boy patronage. The thing stinks to high hell. Part 61 is truly the underbelly of GA.
Have any documentation on how many DPEs were busted? I haven't seen any indication that this was widespread. Around here our DPEs were all just hammered schedule-wise during that push, but I know of none who were booted or who were unfair on rides.
Besides, pilots probably suck at this in general, but if a DPE was busted out, they'd have an excellent small claims case to get a judgement for a refund. It's unlikely a busted out DPE would even bother to show up in small claims court. Summary judgement, done. Then of course one would have to collect, but you'd get it back eventually.