I think he became a HOSTESS/ESCORT not a sex object nor a prostitute because he had no choice since people view them as for pleasure and carriers.The thing you said about "hate being objectified as an omega yet continue working in an environment that frequently attracts alphas who do the very thing he despises" but their place attract people who want to be drunk and someone to talk to closely (like a bartender for every person) so the "alphas who do the very thing he despises" are people who rape and think they're above omegas which are not decent customers. And also again his job and what he was aiming for was clearly stated that they were not sex objects but hostess that make people buy more expensive drink so they can fool ALPHAS to buy more and dry their wallet and as for people like Arisaka and his co-worker they are decent customers.
I am fully aware he was a hostess/escort and his job isn't to have sex with customers. I was just stating that maybe he should work somewhere else that doesn't further perpetuate his being viewed as a mere source of pleasure for many alphas who go there. I know it's much easier said than done considering omegas are at a disadvantage when it comes to job opportunities but he could still try. Like I mentioned earlier though, I have nothing whatsoever against his current job. It's just as you said—his task as a hostess is to make alphas buy more expensive drinks and dry their wallets. Nothing more, right? He even said so himself, "Our place isn't like that." His workplace obviously isn't a brothel so why sleep with those alphas? If it's to prove to them he's not a sex object, it's incredibly counterproductive.
Arisaka is not only honest to a fault, but he's also sincere, loving, and understanding—not to mention incredibly attractive. Definitely one of the greatest alphas/semes out there.
My only issue is with Nanao's mindset. How can someone claim to hate being objectified as an omega yet continue working in an environment that frequently attracts alphas who do the very thing he despises? I personally don't have anything against his job and what he does. However, if he really wanted to prove to those alphas he hated so much that he's more than a sex object, he should have chosen a profession where he can show himself capable of doing other things. Then again, if he hadn't decided to work at that place he might not have met Arisaka...