I went into my draft expecting multi-position players to be at an ultra-premium... I was wrong.
Do they make things easier in the case of injury? Sure... They definitely do.
In order to make them worth "extra", your league and team have to be set up the proper way.
First, the less bench spots, the more important. Flexibility becomes much more important when you don't have as much room to move.
Second, the player themselves needs to be flexible at the right positions. You still need to be strong at shallow positions. Having a player with 1B/OF eligibility honestly isn't much use. Both of those spots are stacked. Likewise, if they're only eligible at two shallow positions (2B/3B), you need to shape your roster during the draft to benefit from that. If you don't have any other 2B option, and your 3B gets hurt, you can't exactly benefit from shifting your multi-use guy over to 3B, now can you? You're left just as shallow at second.
They're not a season-long solution to shallow positions. They're stop-gaps for 15 days at a time. You still need to have good everyday players at the shallow positions if you want to reap any of the benefits that a multi-position player gives you.
As for their added value during a trade (or the draft, for that matter), it depends entirely on the team that they're going to end up on. It doesn't add any value to your team by drafting Rich Aurilia. He's still Rich Aurilia. Just because he can fill a dozen positions doesn't mean he's going to produce anything while he's doing it.