My main concern with these higher frequency connections is that they require a lot more power to run. So we can’t have phones that will last weeks without charging.
That's generally not true.
What does require more power is a higher data rate (which is often available only on higher frequency bands, due to there being more bandwidth), but there shouldn't be any meaningful difference for a constant data rate voice call across bands.
If anything, higher frequencies usually imply a denser network of base stations (since radio propagation is somewhat worse), which means your phone needs to transmit less in the end since there's less distance to cover.
For example, GSM at 900 MHz had a maximum mobile EIRP of 2W, while at 1800 MHz it was only 1W (at the same channel bandwidth).
And either way phones running on 4G LTE or 5G are largely using the same frequencies as before. Few phones actually connect to those ultra wideband networks for any notable percentage of the time. Most of the time they're connecting to 4G/5G towers operating around the same older GSM bands. Those earlier StarTAC phones and the Nokia 5110 ran at ~800-1900MHz. A modern 5G phone on T-Mobile US (Band n71) will operate on 600MHz. On your logic, a modern 5G phone on T-Mobile should work much longer than many older phones.
Well sure, then it's like a tablet in standby, which similarly can last a month or so.
But it's not going to last more than a day or two if you've got the screen on, playing games, watching movies, using apps offline.
Turns out stateful firewalls aren't just a security factor on mobile internet connections.
I did have an experience with my phone being suddenly used by random internet users. I had ampache running on my n900 (maemo/debian-based) and somebody found it on the internet and started streaming my music. :D I had a higher-than-normal amount of battery usage for a few days so I decided to see what's using it and discovered that my music was being played and downloaded.