The problem with the shotgun in Doom 3 stems from a separate issue with all of the guns in general. Typically in other games, different gun types filled different roles. In Doom 3, they were more of a tier based system. The shotgun replaced the pistol, the assault replaced the shotgun, the plasma replaced the assault, and the chaingun replaced the plasma (assuming you managed your ammo). None of the guns really did anything different over the others. It was strictly a damage difference. Reloading speed wasn't really a factor in conjunction to damage output and spread was basically non existent/needed. So the shotgun which was traditionally a workhorse in damage where burst was needed it fails entirely being the second weapon you got and thus the second worst in the arsenal. This was further compounded by how ammo was dispersed within the game. You didn't really NEED to manage your ammo (aside from chaingun) Where in older Doom games, cells were preciouses and generally scarce. In 3, you found enough to pretty much never need to worry about saving for harder fights. Not always of course, but for the majority you had plenty to keep going.

The weapon philosophy in Doom 3 was bizarrely basic.

Typical, everyone wants a piece of the Duke….
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And Doom 3's shotgun is ok, remember, that game takes place mostly in crammed and confined spaces.