Dalglish won things though. Souness didn't last long due to health issues but least he had a few SPL titles behind him when it was a 3 team league. Supporters will overlook a lot of things and make excuses for failure of a favourite, but some of their's turn on Klopp every now and again. If slippy doesn't do well at Villa I can't see how he gets the RS job unless the owners want an Ole type puppet. And even if he did if he has a bad run of results with next to no evidence he can turn it around he wouldn't last long, they are not going to want another 30 year wait for a title.
Dalglish did win things, you're right, but he hadn't at the time.
Souness came in, with just a smidge more than Gerrard did at Rangers, and he's not going straight to Liverpool. Souness also did a solid job at dismantling their dynasty and setting them back 10 years.
Evans, again, more of the same, in house recruit who had money and got nowhere.
If he does a steady job at Villa, I think he gets it myself. In a day and age where it's never been harder to get your hands on a trophy, and there's huge competion even for 7th place and the Conference League, I'd argue, playing good football and being a European Contender would turn heads. If he goes and plays really negative stuff, that's where it stops.
I think Gerrard and Solskjaer would be a poor comparison, purely because Solksjaer got the job out of desperation. The players started playing cause they hated Mourinho, and nothing else for me. I just don't think he'll need to do as much as people think.