Taking OP's sequencing.
1. Passengers can demand anything. There is no requirement that DL have returned to the gate, but most carriers will do so because the reprecussions of having this turn into an incident in the air and having to divert are more serious than a simple ground delay.
2. You can make the argument that this was all in DL's control, although DL might just say that the initial short delay would not have caused a misconnect. However, you may run into trouble with $149 because you skipped asking DL for a voucher. DL pays almost nothing for those rooms and may well only reimburse you what it pays for those vouchers (which can be $50 or less).
3. Why indeed? Because there is no way of knowing who wants a voucher and because someone has to do the preparing. DL does do this on long-haul flights where it has hours to prepare. At some stations, the kiosks are set up so that you can handle rebooking and obtain vouchers without speaking with anyone.
4. How has DL handled your prior A rebooked into Y complaints?
5. Yes.
A couple of easier solutions:
A. Make the claim on travel insurance. It tends to pay up to a fixed amount and $149 is likely well within range. You get that and food and you have a check in a few days.
B. If this was business travel (corporate rate) why isn't this reimburseable by your employer, leaving to your employer --- or TA --- the decision to pursue DL or not?