Fixed quotes work for well defined scope and mitigated unknowns. When things aren't static, when there are too many unknowns, risk (in giving a fixed price) increase, often significantly. I've seen plenty of solo-ists and agencies give the client the price they wanted and then go well into to red trying to deliver.
An alternative is to be heavy-handed in your estimate. Eye it up and 2x it, or 3x it.
Again, the question was: There are too many unknowns. The answer is T&M. Btw, they can be combined. Fixed price on the knowns, and T&M on the unknowns.
Put it this way, I've seen 5x more fixed price projects go sideways than T&M. That's how bespoke work works best.
To get in a price battle with another bottom feeder for a project with too many unknowns (and likely a client with higher-than-budget expectations) is a classic fool's errand.
We all know the rule:
Fast. Cheap. Right. Pick two.