There already are multiple Software Defined Radio transmitters on the market. Pluto, Pluto+ (a clone with increased functionality), Hack RF, and those are just the ones that don't have built-in interfaces, requiring software. Many others exist.
The issue with these radios is spurious transmissions. Some have built-in filters for the VHF and UHF amateur bands, some of the more expensive for the HF amateur bands, but attempting to use them anywhere else would certainly cause interference.
There is one, the Hack RF Portapack (a clone of Hack RF) that appears to be priced reasonably (in the range of the SDR Play receiver only) and that could be the basis for Part 15 experimentation with the addition of filtering. It looks like you can get it in partial kit form for around US$100 on Amazon, more in Canada. It's received some pretty bad reviews, but I think that that's because it's certainly not plug and play. Even the SDR receivers require quite a bit of technical knowledge to get going.
I've been delving more into SDR transmitters. It appears that the best one for Part 15 experimentation would be the Hack RF One. It's available relatively cheaply, even with a metal case. Many vendors sell it as a bundle with antennas, USB cables, etc. but I'd recommend sticking with the basic board. It covers from 1Mhz up to 6Ghz, and does have some hardware filters, although probably not enough to completely reduce spurious emissions.
Unfortunately, the software it works with, Gnu Radio, is one of those container-based things, which can cause all sorts of headaches when running on Windows (the home O/S is Linux). I believe the receiver portion can be operated with SDR# and perhaps other similar software, but that's just going by what I've read (which, as I've found out, is drastically different from reality).
Maximum output is said to be about 32 milliwatts, no specification as to what frequency that is on. That would likely be OK for the AM broadcast band, but it would have to be throttled a lot for the FM broadcast band (although you should be able to do that via the software).
I'm thinking of getting one to play around with, and I would also use it for amateur radio (although I'd need an amplifier to make it usable, even at QRP levels).
Of course 34 mW wouldn't suffice for part 15 AM, and we are prevented from using an RF power amplifier by this rule:
15.204 External radio frequency power amplifiers and antenna modifications. (a) Except as otherwise described in paragraphs (b) and (d) of this section, no person shall use, manufacture, sell or lease, offer for sale or lease (including advertising for sale or lease), or import, ship, or distribute for the purpose of selling or leasing, any external radio frequency power amplifier or amplifier kit intended for use with a part 15 intentional radiator. (b) A transmission system consisting of an intentional radiator, an external radio frequency power amplifier, and an antenna, may be authorized, marketed and used under this part. Except as described otherwise in this section, when a transmission system is authorized as a system, it must always be marketed as a complete system and must always be used in the configuration in which it was authorized. (c) An intentional radiator may be operated only with the antenna with which it is authorized. If an antenna is marketed with the intentional radiator, it shall be of a type which is authorized with the intentional radiator. An intentional radiator may be authorized with multiple antenna types. Exceptions to the following provisions, if any, are noted in the rule section under which the transmitter operates, e.g., § 15.255(b)(1)(ii) of this part. (1) The antenna type, as used in this paragraph, refers to antennas that have similar in-band and out-of-band radiation patterns. (2) Compliance testing shall be performed using the highest gain antenna for each type of antenna to be certified with the intentional radiator. During this testing, the intentional radiator shall be operated at its maximum available output power level. (3) Manufacturers shall supply a list of acceptable antenna types with the application for equipment authorization of the intentional radiator. (4) Any antenna that is of the same type and of equal or less directional gain as an antenna that is authorized with the intentional radiator may be marketed with, and used with, that intentional radiator. No retesting of this system configuration is required. The marketing or use of a system configuration that employs an antenna of a different type, or that operates at a higher gain, than the antenna authorized with the intentional radiator is not permitted unless the procedures specified in § 2.1043 of this chapter are followed. (d) Except as described in this paragraph, an external radio frequency power amplifier or amplifier kit shall be marketed only with the system configuration with which it was approved and not as a separate product.
However the matter of harmonics could be brought under control by a loading coil and 3-meter vertical.
Wow, a complicated way of saying you can't add an external amplifier to a part 15 transmitter.
I believe 32 milliwatts is the output at the antenna. Part 15 transmitters are allowed 100mw input to the final stage, and that is usually 50% efficiency, resulting in an output that is relatively close to the output of the Hack RF. At least not that far off.
The Hack RF does have some filtering, and Carl is right, an antenna plus loading coil would result in more.
I would think that you might be able to build a credible Part 15 compliant AM broadcast band transmitter with the Hack RF, although you would likely never be able to certify it, either in Canada or the U.S.
For FM, too little output isn't a problem, but the fact that the output can be easily modified through software well beyond Part 15 levels means that it also could not be certified. And you might have to add extra filtering at the output to reduce spurious emissions. Hard to say.
As an amateur radio operator, I could experiment with it on 160 meters (pretty close to the AM broadcast band) and either the 2 meter (144 Mhz) or 6 meter (50 Mhz) amateur bands. Too bad neither the U.S. or Canada allow use on 4 meters (70 Mhz) like they do in many European countries. The Hack RF was intended, after all, for low power amateur radio use.
Although...
Perhaps if a SDT was used as part of a homebuilt intentional radiator it might be ok.
http://www.hallikainen.com/FccRules/2021/15/23/
Or maybe...
If an SDT were one of several modules in a modular design (?)
http://www.hallikainen.com/FccRules/2021/15/212/
In the U.S. I would say that that would be the case. Homebuilt takes on different meaning in the world of SDT's, where the lines between hardware and software blur.
Unfortunately, in Canada, that wouldn't be the case. They were going to put wording to that effect in the last version of the RSS210 specification (it was in the draft) but took it out in the final revision.