One of the best things of bazaars is that you could close and re-open them when you want, letting you sleep/be away without worries of buy-mugging.
With the current item market, you have to unlist when you go to sleep and relist when you come back - this process is kinda annoying. Unless you bounty yourself, self-hosp with SED or ipecac every hour, you're missing out on potential buyers from different time zones while your asleep/away. Even selling things anonymously makes me feel anxious since i'll be hoping that I don't get mugged before I come back online.
My suggestion is that when you add items to your bazaar it lists them on the item market for you - no separation between item market and bazaar items, the future item market fee will also be applied to bazaar. The only difference is that you can close your bazaar and therefore remove your listings from the item market. This atleast makes bazaars useful and I think is a better option than the current dead or private bazaars. In other words spending 250 points for bazaar unlocks premium options in item market for more convenient adding/removing items in the item market.
Tldr: Merge bazaar with item market, so that adding items to your bazaar lists them on the item market - no separate category. But you can close your bazaar and therefore remove listings from the item market, so you don't get buy-mugged while away.