Wouldn't Soderling's serve be classified similarly?
I agree, it is to some extent.
One thing that Murray does differently than Soderling is when Soderling starts his serve his ball-toss arm goes straight up/out - almost towards the court. Murray by contrast has a toss where his arm pendulums backwards towards the back fence, before hooking around in a loop to toss the ball. Soderling starts with his weight back and moves forward - Murray starts with his weight forward then shifts it back then forward. Murray has much more forward movement than Soderling, but Soderling has more upward (spring) movement - which you can see in how they end their serves. Soderling ends up on his left leg and goes no further - Murray lands on his left leg and then has to make one more step into the court to get his balance.
Similarly Soderling also doesn't turn his back to the court very much until the very last moment in his trophy pose before launching. Murray has his back to the court as the ball toss leaves his hand. This gives his serve more torque potential which is the upside of doing this (especially for his second serve), but it adds another area where even the smallest yip has knock-on effects for the rest of the serve.
Although I'm not a coach I struggled for years with an inconsistent serve and have seen it many times, especially in juniors. Weight transfers in which the server goes forward>back>forward in such an exaggerated amount are more prone to being streaky in consistency - additionally I think it increases the risk of having an inconsistent ball toss also (with the body moving backward and twisting it's got to be harder to toss as consistently as somene who doesn't??). Many juniors do it perhaps because they're not big/strong physically so try to 'slignshot' their serve more with exaggerated weight transfers... Or maybe they try to model themselves off players with GOAT serves (like Ivanisevic) who are plainly too hard to mimic well for the vast majority of learning players.
While Murray's good serves are utterly fantastic, the variation between his good serves and poor ones is bigger than for someone with a more stable base serve with less back and forth weight transfer like Federer, Sampras, Djokovic, Tsonga. When Murray is in a hole you often see him go for huge first serves - if he's not making them he too often backs them up with patchy second serves.
As I said above, this is a matter of degrees - nth degree comparisons between guys who have great serves. It's just my take on why Murray has had the same serve issues for his entire career. They're hard to address when the same minor aspects which make a serve a (comparative) liability at times are the same things which make it a weapon. All he can do it recognise
when the issue is creeping in, take a few seconds longer to clear his head, ignore the situation and hit as he does in practice. This is an areas I think Lendl has helped him most -
hitting out and, as Murray says Lendl has told him, not going down with your back to the wall trying to chase down balls.