A lot of imperial princesses did not marry. I am pretty sure it's most (or, by some periodization of the Sengoku, all), but I can't be 100% sure without doing a physical tally, and there seem to be slight gaps in the record for the early Sengoku (I think it's likely some of these are princesses who died young).

Once we get to the really late Sengoku/early Edo (depend on how you count it), we start seeing marriages between imperial princesses and members of the five regent families. It appears to be a practice that continued into the Edo period. In other words, the choices were marry someone from an imperial family (now that they stopped throwing all the non-heirs into monasteries we have other branches of the imperial family again) or one of the regent families (also a lot of regents began to adopt imperial princes as sons), or be a nun.

Daimyōs are far too low rank to marry an imperial princess, though politics (succession, de-facto rules, function, and diplomacy) and economics (the imperial household was so poor that they didn't even have official empresses, and a lot of positions went unfilled) likely came into play too. The most daimyōs can hope to get are members of the mid-high aristocrats. IIRC, the only case of someone from a warrior family marrying an imperial princess is Princess Kazu marrying Shogun Tokugawa Iemochi in 1862, way past our time.

Unfortunately I don't have an English source for this. Lee Butler's fantastic Emperor and Aristocracy in Japan, 1467-1680 - Resilience and Renewal have short sections on aristocratic women and the functioning of the imperial household, but not imperial princesses themselves, and if he doesn't have anything I don't know where else to look. If you know Japanese and want to look these up shoot me a PM.