You'd see a lot of people suddenly become more conservative Democrat types, just like Lieberman did between 2006-2010. Some issues, like Obamacare, would get restored back to how they were originally, but I wouldn't be surprised if they didn't bother with a public option even with a supermajority. You'd see a lot of efforts to involve the Republicans, who would dutifully gum up the works and delay everything. Just like 2006-2010.
In this hypothetical scenario, would things get better? A lot better, even? Sure. But the sort of People First populist transformation that so many people in America have clearly been hungering for since the Bush administration would not be addressed. Labor rights in our little fantasy wouldn't be overhauled. Some major environmental legislation would almost certainly not be enacted. A major overhaul of economic philosophy, which is ultimately what we REALLY need, would not be done. They would just work to make the already broken system slightly more tolerable.
Why do you think so? I tend to think the opposite, the party and the country has shed more of it's post-Reaganism resistance to socialist ideas(I wouldn't exactly agree the country has longed for them since Bush), and a super majority in that environment would also theoretically reflect that. Plus, as supporting evidence, when you looked at the super majority House back in 2009, they were out there passing much more comprehensive types of reform, including cap and trade and a public option with much stronger reform structures, and would of easily gone further if they weren't pre-empting the response of a fragile veto proof majority in the senate and a determined opposition party. In fact, if you go read the critiques of that period, Pelosi was hit with using her disproportionate majority too strongly with regards to what the Senate could muster given the weaker majorities. The problem was the very few centrist Democrats like Lieberman and unified Republican opposition. Even as you say, the issue with super majorities is the lack of numbers to over-power the other guys.
You are probably right that they aren't going to be implementing some sort of wholesale socialist agenda, but I think its pretty safe to say that a super majority, in today's environment, would push forward a ton of needed reforms, and that is the sort of situation you are going to have a much easier time lobbying and influencing then some Republican regime. You aren't ever getting campaign finance reform passed on the heels of Republican majorities, or climate change legislation, or increased labor protections, or a public option.
Frankly, procedurally, one of the ironies of this era of Republican's breaking all these procedural norms on things like ACA repeal and tax reform is that it makes things a whole lot easier for Democrats next go round. It's really hard to stay within the bounds of the Senate parliamentarian on the AHCA McConnell wanted to pass to say at 50, it's actually a lot easier to pass something like a public option, Medicare and Medicaid buy-in, under that arrangement. And now that the Republicans attacks on procedure and their subsequent abuse has eroded any legitimacy Democrats felt from attacks of that sort, there is little reason to think Democrats will be swayed against that pathway next time.