Yes… the thing is that with asexual reproduction you can reproduce way more and much faster… so even though each individual division might have less variability, you have many more generations of splits and a bigger population that ends up being forced to spread around more to different conditions and eventually leading to mutations faster than they would have otherwise.

Also, the ease of reproduction makes each individual more disposable, and at that point it doesn’t make as much sense to have more mechanisms to protect your genetic material from mutagens, you can just let the mutants die when they are not fit and produce new ones until ultimately you hit the jackpot and achieve a new resistance. This is what makes bacteria so adaptable, with new strains appearing every day.