SSRI have severe sideffects, but mostly of the kind that doctors strangely seem to think of as harmless, such as the well known and quite common loss of sexual interest, which kills quite a few relationships. Even worse there is growing evidence that it occasionally causes a permanent reduction or loss of sex drive. The group who self identify as asexual have almost all been prescribed SSRI as young teens, and this might well be causation, not correlation. After all, if you got SSRI as a kid and then never felt your sex drive before it was permanently lost, how would you know?

SSRI are almost mostly ineffective, with roughly 70% not responding at all. They were however heavily marketed as the patented, and very expensive prosac for decades and more importantly while they occasionally treat depression, they feel bad to use and are never used recreationally, and thus avoided the moralizing around drugs. Not to say the marketing wasn't needed, people were highly sceptical of using chemicals to treat depression, especially as people occasionally melted from serotonin storm before they figured out dosages and cross interactions.
Doctors are restrictive in which alternatives they try, not because they are afraid of side effects, but because off label use requires personal responsibility, and is often against policy one way or other. Good alternative treatments include hallucinogens, in particular ketamine and peyote in large single dose treatments when not taken in a clinical setting but with friends. These have long been avoided despite good evidence they work astonishingly well for depression. This is partly because of the war on drugs propaganda and moralizing, but mostly because these hallucinogens cannot be patented, meaning its not worth the price for the large manufacturers to do the marketing to overcome the anti drugs propaganda. Its not random chance that they are currently trying chiral variants, partial ingredients and various anti hallucinogens and treatment schedule combinations of these, despite all evidence so far indicating its all worse than the well studied plain unpatentable medicine.
Another example is Amphetamines which in typical doses prescribed to children with adhd treat the primary observable downside of depression i.e. low energy, low focus, loss of work, reduced activity, etc. Unsurprisingly, the subgroup of depressives which respond well to exercise roughly a third, respond very well to treatment with amphetamines. As anyone who ever considered maybe working out, but not really wanting to, and then took amphetamines will tell you. With amphetamines, its almost certainly not a direct treatment of the depression, rather it facilitates changing habits in such a way that a common pathway out of depression is more likely to be taken. They have a significantly increased likelihood of suicides compared to hallucinogens, but the effect is comparable to that of SSRI. The main sideeffect of therapeutic/low doses of amphetamines is weight loss, a mostly desired outcome. So excluding people with easily tested for heart problems and trivial to identify anorectics, why not try it... Well its war on drugs propaganda again...

Doctors have a nasty habit of thinking they should make the judgement regarding the tradeoff between various treatment, instead of presenting the options to the patient and letting them decide. But the real problem is idiotic moralizing around "drugs :O".