I have had the first shot of a burst turn out well, but it is not something that happens frequently enough to make me avoid bursts.

I used to shoot events for PR for an organization I belonged to. There were frequently shots of someone at a podium, speaking. There were two guys, high up in the organization, so they were frequent subjects, who would contort their faces into the most amazing expressions while speaking. Their face could do that in the few milliseconds between deciding to take the shot and the shutter opening. The ONLY way to get a good shot of either of these guys was spray and pray. Many times I would take 3-5 shot bursts, winding up with 50-100 shots to choose from.

Another thing I encountered was when doing group shots with flash. Many times I would encounter a blinker. There are two kinds of blinkers: most frequently someone will blink in response to the preflash and their eyes are closed when the shot happens. Another kind has a delayed response, so they will blink after the shot. The first kind is addressed by raising the ISO to the point where it doesn't affect the IQ too much but allows the flash to loaf so it doesn't dump all the charge in one flash. Then you can use a high speed burst and get 3-4 shots of the group on a single charge. The first kind of blinker usually recovers by the third shot and you can get their eyes open. If you have both kinds of blinkers in a group, it's tough to get everyone with their eyes open in one burst. If that happens, the only remedies I have are (1) take longer bursts; (2) swap heads in Photoshop. Since you took a fast burst the background doesn't change much so it's really easy to swap heads without worrying much about the background changing.

Sometimes multiple shots are necessary.

This is digital. The shots are essentially free. The cost of a shot is (1) amortization of the capital costs of the equipment (so the more you use it, the less the shots cost); (2) your time in selecting the shots. The second cost is the most important one. However, multiple shots provide some insurance for those shots that are nonrepeatable.

I do not think you folks realize that the first shot should be used as a Polaroid.

If you are a true adept of photography, you would know that the first capture exposes (1) everything that is incorrect in the scene. The following shots are made consequently and reviewed with a critical eye in order to adjust details that might be minor but are issues that need to be fixed before going to the lab (PP).

Burst shooting is a joke unless you are shooting an object moving at a high velocity or is ephemeral in nature.