I don't know if this is specific to this a/b/o universe or not, but I'd image that suppressants, especially injections, are eventually very harmful to an alpha or omega. Side effects and/or eventual resistance to the drugs likely makes ruts/heats feel worse during the times you're not on them and strains the body a lot - imagine birth control x5.
For an alpha in this universe, if you don't take them and don't have sex, your brain goes to hell. If you take them, your body goes to hell. So from my understanding, basically suppressants are a damned if you do, damned if you don't type situation.
(I'll go back through to see if this is correct in this universe tho gotta find my sources)
Personally, I'd also find "it's this or sex" very mentally damaging as well.

That chase understand how bad suppressants are more than anyone else lmfao