I think none of those is true. People (including me) running esphome ble proxies without any problems. Guess most of the users don’t bother about static IP’s (why should one waste time with this if there is DHCP?).
Are you aware that devices always have a IP address and that a hostname is something different?
I expect you didn’t yet read the esphome docs?
Also additional tip if you want to “see” a IP address:
BTW: One of the ideas of esphome (together with HA) is to completely avoid wasting valuable time with IP management but rather (best case scenario) just have things automagically discovered thank’s to mDNS 
And another one for you @nhaas
Special attention to: 
Format it properly