What you experienced was an IDB. The first bit of advice I can give you is that unless you see a seat assignment on your boarding pass, you aren't guarateed a seat. Sometimes, a call in to DL customer service to explain the critical nature of your arrival on time can help you get a seat assignment early. Also, DL now offers Preferred Seats for sale at time of check-in, so if your arrival on time is critical, that's a small price to pay to avoid missing an important appointment.

IDB compensation was just increased, IIRC, to a minimum of $650. I haven't really had time to look over the new rules fully yet, but it goes without saying that DL should have offered you compensation. In terms of the letter of the law, that's all they had to do.

DL, like almost every US airline, oversells its flights. This serves two purposes: one, it ensures that flights go out full, and two, it allows for spillover onto off-peak flights that may otherwise go out with a lighter load. Factor into mind that many passengers will jump at the $200 voucher they offer, and overselling is a win-win for the airlines. They realize additional revenue, they move passengers onto lighter flights, and the VDB'ed pax are stoked because they can now afford that flight to Vegas.

Prioritization of standby passengers (which, unfortunately, is what you are if you're carrying a seat request card) is based upon Medallion status and fare class. To make a long story short, if you're a non-Medallion on a discounted economy fare with a seat request card, I'd start making phone calls to push critical appointments back, because DL will probably not be able to accommodate you--Medallions and higher fare classes come first.

It stinks if you've got somewhere to be and no one's taking the VDB bait, but terms of IDB are spelled out in the contract of carriage (the fine print on your ticket). As long as Delta adhered to those terms, they did what was legally required of them, unfair as it is to those still standing when the game of musical chairs ends.

So, my advice going forward:
1. Check to make sure seats are available on the flights you want before booking them.
2. If you don't have status on an airline, any airline, don't book the last flight of the night unless you can confirm into a seat assignment at time of booking (you should be able to choose your seat before buying the ticket on any airline that assigns them).
3. If you're flying DL again, check in at T-24, the instant you can, and buy yourself into a preferred seat to make sure your seat request becomes a seat assignment.
4. If all else fails and you're being IDB'ed at the gate, make sure you know the DOT regulations for IDB compensation, and make sure those are adhered to. If they're not by the GA, ask for a supervisor and insist that if you don't receive the proper IDB compensation as spelled out by the COC, you will be forced to file a DOT complaint against the airline naming the gate agent and supervisor as the offending parties representing the airline. I had to make that statement once when flying United a couple of years ago, and much to my "surprise", they noticed that there was still a first-class seat open after all upgrades had been processed, and decided to go ahead and put me in it.