ImAIdoot
Interesting point of view but I'm not sure I quite agree.
First of all, you haven't addressed the issue of electoral reform, which I see as being absolutely fundamental to addressing the democratic deficit in the UK. Absolutely nothing in EU law would prevent the UK from adopting a more representative electoral system. For anyone concerned about democracy and accountability, in my view this is what people should have been protesting about and campaigning to change for decades now. Forget the EU for a minute - what the government (and to a lesser extent, parliament) does has a far greater impact on our lives than anything the EU does. If you're serious about addressing a democratic deficit, you should start with the most serious one, and that is the one in Westminster.
Secondly, we could adopt a written constitution if we wanted to. Yes, it would clip the wings of parliament. It would be a profound constitutional change. At the moment parliamentary sovereignty is the bedrock of our constitution. Public discourse seems to accept that this is unambiguously "a good thing". But when you combine parliamentary sovereignty with the first past the post system, this means that in practice, someone voting against the majority in a safe seat has absolutely no meaningful democratic representation at all.
In Ireland they have a written constitution which can only be amended by referendum. This reduces parliamentary sovereignty but gives the Irish people the ability to decide, on a one person one vote basis, on issues of fundamental importance to them, such as whether same sex marriage should be legalised, or whether the constitutional ban on abortion should be removed. It's not a perfect system, but I can't help but feel that in Ireland, the people have more power than they do in the UK.
The animal welfare issue is a tricky one - I don't believe that a significant number of MPs care all that much about reforming animal welfare laws, and this for me highlights the general disingenuousness of the Brexiters. People like Michael Gove are quite happy to blame the EU for why they haven't done things that they never had any intention of doing in the first place, and now we are leaving the EU he can say "now we can have better animal welfare laws because we are taking back control from the EU?"
Can we? Maybe. Will we? I doubt it. Especially if we do a trade deal with Trump. I attended a Q&A session with Michael Gove shortly after he took up his current post and someone did actually ask him this very question. He squirmed out of answering it.
As to your last point, this has been said many, many times before but it bears repeating:
The ECHR has nothing to do with the EU.
It is a completely different legal framework. The only link really is that being a signatory to the ECHR is now a prerequisite for accession countries looking to join the EU.
As things stand, we are not looking to withdraw from the ECHR, although there are many in the Conservative party who would dearly love to do so. As far as I'm concerned, if there is any sign than we are seriously contemplating withdrawing from it, that really will be Worth marching on the streets for.
Human rights laws are largely there to provide people with inalienable rights which cannot be interfered with even by their own elected government. (Especially by their own government, given the nature of the rights in question.)
So this is one area where parliamentary sovereignty definitely should be restricted, and an international legal framework in which people can enforce their rights in an international court is of utmost importance.