From what I’ve seen (see Harald Welte’s 33C3 talk (video, slides), also a Sierra Wireless press release and some reading on the Option modem which the GTA04 used), there are several vendors who basically stick a wrapper around a Qualcomm modem and package that out as a complete system. What this means is that the choice of actual baseband chips is strongly limited to a small handful of vendors.
That said, it was discovered that some USB modems (Ralf-Philipp Weinmann’s 30C3 talk) with a QC chipset at their core did not check firmware signatures, and neither did a small subset of Samsung Galaxy S4 phones.
I don’t know whether this remains true for newer chips, but I don’t expect it to be a common occurrence and realistically, a modem manufacturer is not going to release a special version of their recent hardware with no signature checking to what is quite frankly a very small niche market.
I’d like a fully programmable baseband chip. I really would. Unfortunately, the only “legitimate” feasible way to do that would be to get some kind of integrated SDR and while this is possible (it’s what Icera did for their modems), the only similar thing I know of which is designed as open hardware is the XTRX (an FPGA-based Mini PCI-E device) which is too large and too power-hungry for a phone. Not to mention that we’d still have to write a full GSM/UMTS/LTE stack.
A more underhanded approach would be to use a commercial chip on which we know there exist arbitrary memory read and write commands (for instance, Samsung basebands from Nico Golde and Daniel Komaromy’s REcon 2016 talk, slides and video; also possibly older Qualcomm devices through some of the DIAG commands, see Guillaume Delugre’s 28C3 talk, slides and video) and then either NOP out or, with somewhat more coding prowess, rewrite the more offensive components of the cellular stack… but I don’t imagine that the baseband manufacturers would take too kindly to relatively widespread console hack-style alteration of their stuff.
In short, yes - as mentioned just above me, the best we can realistically do is what is currently planned for the device.