Actually, golems would be more likely to cause strain to us since:
a) it costs much more magic to animate a golem than a corpse.
b) we would actually have to control them ourselves, instead of leaving the job to spirits, since we don't have enough useless memories to feed them with. On the other hand if we can use rat memories to recruit rat-level spirits and they are happy with eating animal memories, then we have a self sustaining population that can go out and hunt vermin for food, at least until we run out of rats in the city, which is very unlikely. There's bound to be hundreds of rats here, so a few dozen undead rats should hardly put a dent to their population.
And they can't become a plague because they can't posses corpses and multiply on their own, they need us to perform the reanimation, at least as far as we can tell.
Furthermore, if an undead rat is seen during the attack by, say, a civilian that happens to be nearby, then:
a) they might not even notice that they are injured in the darkness.
b) they are much more likely to be horrified and scared and run away before they notice they are injured.
c) even if they do notice they are injured, they might just attribute it to rabid rats that keep attacking even after their target has injured them.
Best case scenario they never suspect a necromancer is involved and attribute the attack to wild animals. Worst case a necromancer is one of many possibilities. Hopefully not something that warrants a deep investigation unless more incidents are reported.
On the other hand, trash bags that move around on their own are very definitively supernatural, so anyone that happens to witness them would be likely to report that. Not to mention the fact that depending on their method of attack, there might be blood involved. Best case they think necromancer is one of a few supernatural possibilities (e.g. telekinesis, if that's a thing in this world). Worst case they are certain it's a necromancer because golems have a specific way of moving. Either way, an incident that certainly merits attention. Unless they just dismiss the testimony as absurd, but given that this is a world where the supernatural is most definitely real and everyone is afraid of (or at least knows of) necromancers due to state propaganda I wouldn't get my hopes up.
If we are to use trash golems we should at least perform a test on their cost, strength and durability to see if it's even worth it.