Is this actually true? I've seen this repeated in many comments over a decade, and whenever it's researched it turns out there is no basis for it.
The usual conclusion is that the manufacturer claims that they cannot allow open access to their radio because of licensing restrictions, but that no restriction actually exists. It's a lazy way for them not to bother.
You can buy a board from Ettus Research and write your own baseband software. The trick is that you need a license to operate a radio at those frequencies, if you buy a phone you get to tag along on the phone company's license because they have made sure that you can't do anything that they didn't show the FCC they could do. If you have an Ettus board and you want to run a base station or an edge device you need to get a license from the FCC to use it.
Strictly speaking, the phone company could have an "open source"[0] baseband stack and they would need to provide some way for the phone to know that it is running the approved version. And that is where it gets tricky, how do you do that? You could provide some sort of EFI type signature on the baseband bits that proved they were the right bits, and you could provide instructions on how to compile to exactly those bits, and while that would help folks understand what could and could not be done with the firmware it wouldn't help them fix problems. And of course people would scour it for vulnerabilities. So we're left with the current situation.
If you're interested in playing around with radio stuff though it is pretty straight forward to get an amateur operators license and a Gnu radio kit and start exploring.
[0] -- Not 'freely licensed' so much as 'you can read the source code, and it is compilable from source'.
You would still have to trust the manufacturer that it didn't implement fake reporting of well-known signature while in fact using something different. Pointless.
Well there ARE FCC restrictions on what frequencies you're allowed to transmit on. Most frequencies are "owned" by someone that has the right to transmit cell phone, radio, television, or other data across them. You may recall, for example, that there was a big bidding war several years ago when some of the old UHF bands were sold off. There are some open frequencies which you're allowed to broadcast without a license on, these are the ones that your cordless house phone and such will transmit on. Whether or not this is a legitimate reason for the closed source antenna code is beyond my scope of knowledge.
what good is such increase, if client (un-altered, standard Tx power) devices will hear router from afar, but router will not hear their replies from the same distance?
I think the truth lies somewhere in between, so you'll never find an explicit 'basis' - manufacturers are worried that publishing radio source code and encouraging open access will subject them to FCC requirements for any possible "end user modification" rather than just for the straightforward simple behavior they've programmed.
The usual conclusion is that the manufacturer claims that they cannot allow open access to their radio because of licensing restrictions, but that no restriction actually exists. It's a lazy way for them not to bother.