There are certainly several SDRs that cover a lot more than just a few ISM bands, from LF through to GHz.
They are primarily designed as radios though, and when used as test equipment one should be aware of that. This is not necessarioy a limitation, it's just that they aren't designed to give accurate absoulute measurements, and they are not accurately normalised in the frequency domain in the way that an SA typically is. As a radio, down at HF and below there is so much ambient noise that paying attention to getting single digit noise figure in a receiver would be nothing more than an academic exercise with no practical benefit. The same is not the case at VHF and above where single digit noise figure is expected and demanded. In an SA on the other hand more attention is given to maintaining a constant and accurate absolute reference across the frequency range, and sensitivity is very much a secondary consideration.
Having said that, SDRs can certainly give accurate relative measurements at a given frequency and within a certain limited span, and give accurate sensitivity and noise figure measurements too with the right software (and a calibrated noise source in the case of measuring noise figure). If you have an accurate RF signal generator, you can use that as the reference for your SDR to give an absolute. measurement.
In general, I'd say an RF signal generator is generally going to get more use than an SA, but that's like comparing apples and oranges. And anyway, an RF signal generator doesn't look as sexy as a Spec An on the bench.
FWIW I use an Anritsu MT8802A with the spec an option, option 7. They offer a 300kHz to 3GHz range for RF signal generation, RF power measurement and spectrum analysis in one package. They're frequently on ebay, they were bought by cell phone manufacturers in large quantities, and that's reflected in the user interface, but they are also extremely useful for basic RF analysis, production testing and fault finding. It's the RF signal generator that gets used by far the most out of its functionality.