I assume thermal instability comes from inadeqote cooling.
No. The thermal instability discussed here has little to do with external cooling - it's about local hotspotting, which happens so quickly and at microscopic level that it's all about the
internal heat spreading of the die, through the substrate, to the device case. You can't do much externally.
This is, as has been explained numerous times, due to the different threshold voltage of the different parts of the transistor, and their positive tempco, meaning that a local part that takes more current through it, starts getting even more current, and runs away thermally.
This is actually the same discussed problem of Vgsth matching, but you can't do anything since it's happening inside the transistor - and they have done their best to
minimize the source (emitter) resistance. Can't add separate amplifiers or emitter resistors there!
This effect
is rolled into the SOA, and if your part has a DC SOA graph like this one, and it's OK for you, then go ahead. (Although it would be still quite difficult to be in-spec if they only give you a DC SOA for Tc=25 degC. You need a refrigerator cooling, basically. Or you are going outside the specs and are on your own anyway.)
Otherwise, the manufacturer is outright lying, or have no idea about the basics of their field of market.
There is only one problem, and it's the fact you can't believe a manufacturer could actually lie about their parts - or if not outright lie, at least not understand their own parts and what the basic specifications means. When you gain more experience, you'll find out the harsh truth. They lie all the time. And the datasheet writers are not always the brightest geniuses who actually make the transistors. Wrong info on the datasheets is so common that it isn't even a pet peeve of mine anymore - we just need to live with it. It's like a rainy day, we don't even feel like complaining about this would help.
This being said, the chances are the DC SOA is perfectly valid. Go for it.
Vgs (Vge) threshold matching is completely a red herring. There is zero need to match this parameter. Any sane design today uses separate drive per transistor, completely eliminating this parameter. Not using a separate driver is an ugly hack, only there to try to "save cost", which made sense when opamps did cost something. Now they come in miniscule packages and cost a few cents per amplifier. Now, not using dedicated drives only
increases cost as you probably need to derate the transistors more, add more source(emitter) resistance, handpick parts or do some other hacks which have their own hidden costs (most likely much more than an opamp).