I've had a money tree plant for years now. Had some ups and downs but it's doing well. Lots of new leaves, growing tall, etc. I've had it staked to keep it standing nice and straight. But in adjusting the stake recently I realized the plant is totally unable to stand on its own. Like it would bend double and be in danger of snapping without the stake — which seems like a bad thing, no? Should I be concerned? Any suggestions?

If you dont mind keeping staked, then I would say it is not a problem per se.
It would be a tree in its natural setting, given the right conditions. Those conditions arent quite met in a typical home.

Inside, there is no wind to force a trunk to strengthen. Once a plant grows taller than the available window, the top can not get as much light. If you put the pot on a much shorter little table, or on the floor, that would lower it so the top can get more light.

So there's nothing to be done to strengthen the trunk — which is not a problem?

A stake will keep it in a more upright and when more of it turns woody with age, it should stay in that position - but by the time that happens, the new growth above will be as weak and floppy. Blowing a fan on it can help prevent leaning, especially in combination with periodically rotating halfway, but the effectiveness on an already leaning plant may or may not be enough.

Trimming some leaves from the low side can help remove some of the weight. Trimming some of the height would also remove some of the weight and might help alleviate some of the lean. Impossible to gauge that before trimming is done. Once it gets taller than the top of the window, the top won't be able to get enough light.