> will a tower with a band 66 antenna give this modem some of the central band 4 subset, or will it try to negotiate a channel that this can't access?

Here in the US (and likely in other places), carriers use MFBI[0] to solve this issue - it lets them broadcast both AWS-1 (as B4 and B66) and AWS-3 (as B66 only).

This first came into use when AT&T wanted to use B17 (Lower 700MHz blocks B-C) for their LTE network, rather than B12 (Lower 700MHz A-C). This prevented users from bringing their phones to smaller carriers (T-Mobile and US Cellular), who had significant 700A holdings. The FCC eventually pushed ATT to use both B12 and B17.

> little-used ATT bands

This phone likely wouldn't work on AT&T anyway - despite California's SB822 [1] forbidding it, they whitelist only specific devices on their network, and can go as far as soft blocking your account if you have one that is incompatible. I've linked the compatible phone list[2] below.

SB822's net neutrality provision has already been upheld in court (AT&T subscribers lost "data-free TV" on AT&T owned platforms because of it), but it remains to be seen whether other provisions (bans on tethering restrictions or device whitelisting, for instance) will be upheld as well.

That said, one nitpick I'd have is that these bands aren't necessarily "little-used" - B14 is FirstNet spectrum, and AT&T is currently rolling it out to a point where it reaches 99% of the population indoors. That's a strong commitment, and the band's support for HPUE means it can support coverage further than others at a similar frequency. B30 is WCS, which AT&T uses for capacity in a lot of places - but at 2300MHz it's not particularly useful for coverage. B17 is irrelevant due to MFBI and B29 is supplemental downlink (only useful for capacity).

It's important to think about the carrier aggregation combos that this device supports too - for folks who live in cities, carrier aggregation means a significantly more usable experience when the networks are congested. I don't see a supported list for that modem online, but it would depend on which are enabled in firmware anyway.

> 600 MHz T-mobile band 71, which has a wide rollout but poor device support.

As for T-Mobile; Band 71 is necessary in a lot of places, because they've been spectrum constrained for a long time. Until the 2017 auction for this 600MHz spectrum (which was rebanded from Digital TV service), they had no nationwide low-band holdings (unlike AT&T, who held many 850MHz Cellular licenses from decades ago, and Verizon, who won nationwide licenses to the 700MHz Upper C block in 2008). In 2015, they picked up licenses in the the Lower 700MHz range, mostly exclusive to A block - but they acquired almost none in US Cellular markets (much of the midwest, and parts of the northeast/northwest).

It's difficult to build out a network on midband alone - cell sites must be spaced far closer, and in-building coverage is very poor. This was one of T-Mobile's main limiting factors for a long time, and they didn't truly resolve it until that 2017 auction.

T-Mobile had a reputation for a long time for dropping service as soon as you entered a large building - this is why. Physics mean that lower frequencies are useful to telcos because they travel further, while higher frequencies are useful because they can carry more data.

The post-auction DTV transition wasn't short - it happened over 9 or 10 phases, which extended from 2018 until early 2020 (and were then extended again, due to the pandemic). This is part of why phones seem to have poor support - the 600MHz band is not widely used for cellular outside of the US and Canada even today, so it's common on popular phones made for those markets[3], but not in more niche devices like the PinePhone.

[0] Multiple Frequency Band Indicator (https://www.phonescoop.com/glossary/term.php?gid=551)
[1] https://leginfo.legislature.ca.gov/faces/billNavClient.xhtml...
[2] https://www.att.com/idpassets/images/support/wireless/Device...
[3] https://www.tmoband71.com/