Totally agree with your first para, there is plenty of Ukranian propoganda (although I think we'll find a lot of their SF / recce teams have had a successful and outsized impact) but your last bit is the point: you only need to be better than your adversary. The rest is overfitting.
I don't agree with your second point: the early SF model was driven by a number of people who are
exactly the kind fitted to the modern battlefield, and who are in it in many places, it's just they aren't British, American or German any more. At some point we are going to have to address the the thorny issue of what winning is worth. LOAC is only going to be the guiding principle of warfare if the side that obeys it actually wins, and the one that ignores it does not. Unlikely that much of the Ukrainian fighting over the past six weeks has been what the UK considers "suited in the context of modern LOAC".
While I don't doubt the increasing volume of correlating reporting about SEALs etc, the objections seem to miss the point: none of the violations being reported had anything to do with increasing operational effect (i.e. winning), often exactly the opposite. The real question (also avoided in the US discussion over torture) isn't: should we condemn things that are morally wrong but ineffective. Obviously yes. It's: should we condemn things that are effective but morally wrong?
For anyone who reflexively answers: yes, of course, then I'd like to have a conversation about use of stand-off airpower, BDAs and the degree of clinical accuracy implied by "surgical" strikes. Where is that line drawn exactly? Answers accepted in either collateral damage, wedding guests or children, but you have to show working for the conversion. How much is that a moral decision driven by logic, and how much is just the norms we've become used to from hand-waving the real question and costs?
There is a near total failure to seriously address these questions at almost any level, certainly publicly but in my experience not much better privately, instead hiding behind fig leaves like LOAC. As the Ukraine war has already shown, those will disintegrate within days if a serious war ignites. The lesson from the SEALs stories is that the time to address these questions is now, not to hand-wave platitudes that will instantly disintegrate under pressure, and once again leave future soldiers on the ground as the bag carriers for failed leadership today.
PS I wasn't clear. You make two false dichotomies by conflating "career soldiers" with "lawful", and "old model SF" with "unsuitable". The correct metric is competence, but if you prefer legality, then the SEAL stories demonstrated that professional careerism often exacerbated problems and encouraged cover ups. Plenty of research shows the inclination of group cultures towards conformist corruption and that whistleblowers tend to come from outside. The old model (WW2) SF teams would be structurally more resistant to unlawful behaviour, not less. So totally disagree with that characterisation.
Where military professionalism is required is in knowledge / expertise (mostly to avoid reinventing the wheel), liaison with the rest of the military machine, and planning. The biggest problem smart outsiders have is knowing what to do and how to do it, but being unable to get approval. But those don't either imply the structures we currently have, nor do they negate the old SF model. In fact, where the old SF model worked, it often did so because the career military contribution was an apposite combination of senior sponsorship, resourcing and then extreme delegation.
I'm not sure that's the lesson I'd pick up from it, but I think we need to wait until more has emerged in open source about exactly what's happening on the ground before we decide what to take from what's happening. I also think at the moment we may be overplaying just how good Ukraine is while underplaying how much of the result is due to poor Russian performance.
On the broader point, you need to have a grounding in military discipline and if you're going to be trusted to use lethal force. This is especially true if you do it in a more disaggregated fashion. The early SF model functioned in a very different political and legal context, and was driven by a number of people who would be entirely unsuited to any kind of work in the context of modern LOAC.
You don't need the entire force, or even the majority of it, to look like career soldiers/officers but you do need at least a small core to come from that background. The SEALs have struggled with this for a long time and I think will likely continue to do so. Arguably they have the worst possible model - direct entry, but through a particularly long pipeline that removes originality and moulds new entrants to fit a very specific culture.