If I have to relinquish my sexual function and grow breasts to reduce baldness, then baldness is not a solved problem.
Low-dose topical application doesn't have those problems. Heck, even "dose your entire body" doesn't always lead to sexual dysfunction. (And breast development is a rare side-effect that you'd notice before anything permanent happens, and is easily-addressed.) However, it is topical application of a medicine that can interfere with fœtal development.
Oh, almost forgot: any messing around with sex hormone levels puts you at risk of depression. That's big side effect #3 (though again, many people don't even notice it).
out of curiosity, what else would you expect the side effect profile of something mediating the effects of a potent androgen on the body to look like?
it's not estrogen where you would expect breast growth (and can't count on any particular changes to sexual function anyway), it's inhibiting conversion of testosterone to dihydrotestosterone which could have that effect, much like you could spontaneously develop gynecomastia without intentionally fiddling with your hormone balance. calling it unsolved sounds a lot like calling the very many conditions with medications that have more likely and worse side effects equally unsolved.
> what else would you expect the side effect profile of something mediating the effects of a potent androgen on the body to look like?
That's what the patient information sheet is for, and why everyone's supposed to have access to a trained medical professional they can freely consult for things like this.
> it's not estrogen where you would expect breast growth
Actually, it is. Reducing DHT levels causes the body to elevate both testosterone and œstrogen levels, via homeostasis. But yeah, it's not a direct effect, and if it's a problem you can twiddle further to make it go away. (You could even do that pre-emptively, though you normally get days and days of warning before breast development actually starts, so I'd advocate the "wait and see" approach.)
A condition is typically considered solved if there are drugs or procedures that cure it and either (a) have extremely rare side effects, or (b) have side-effects that are not as big a problem as the condition they are curing. If a pill existed that cured trh common cold but had a 1% chance of giving you cancer of the throat, people wouldn't proclaim "we've cured the common cold!".