The reason Brexit is a "whole sorry mess" is not because of Miller, it's because Brexit is a highly complicated, controversial, contentious issue and we still have no specific objective agreed among Leavers (what Brexit should look like), let alone among Leave and Remain, all these months/years later.
Miller 'merely' confirmed what should have already been known to all concerned: that Government may not change domestic law unless so authorised by statute (Parliament-made legislation). The referendum legislation and result did not give the Government such authorisation. The Government may have intended to proceed without authorisation but had no legal right to do so - if they had proceeded without Parliament's authorisation they would have committed a constitutional wrong. If Miller did prevent the Government from committing a constitutional wrong, Miller is hardly at fault for the consequences.
We can only speculate what would have happened without Miller, although I think we can be reasonably certain that Parliament would have involved itself if Miller hadn't happened. That said, Miller is useful support, useful ammunition - it's powerful to have judgments from the High Court and then Supreme Court on your side, even though they don't say anything new about the constitution. Likewise, for some people it's a convenient fiction that Miller is to blame. They may even believe that.
But Miller did not give Parliament a new power. Nor did the judgments prescribe a process beyond saying 'our constitution says the Government must seek authorisation from Parliament to change domestic law' (I paraphrase). There's nothing in the High Court or Supreme Court judgments about "meaningful votes" and whatnot - that wasn't what the case was about. The judges didn't say Parliament must debate this in dozens of stages for nearly a year. They said, "For the reasons we have set out, we hold that the Secretary of State does not have power under the Crown's prerogative to give notice pursuant to Article 50 of the TEU for the United Kingdom to withdraw from the European Union.
The European Union (Notification of Withdrawal) Act 2017 is the result of that.
The European Union (Withdrawal) Act 2018, the legislation that has led to the meaningful votes etc, was originally drafted by Government and subsequently amended by Parliament during a series of debates and committee hearings because of Government and Parliament's choices. You can read the progress of the-then Withdrawal Bill at https://services.parliament.uk/bills/2017-19/europeanunionwithdrawal/stages.html.
It would have been constitutionally OK for Parliament to give the Government carte blanche with regard to Brexit immediately after Miller or any time since. It has not done so. Why not? Because whether Leave or Remain the majority of Parliamentarians want a say.
It may be helpful to compare/contrast this affair with the European Communities membership referendum of 1975. The Government and EC member states had previously negotiated and agreed in principle the new conditions of the UK's continued membership. The agreement with the EC was ready to be signed and its terms had been approved by Parliament. The referendum legislation bound the Government to act on the result - remain or leave. It was such that no further legislation was required to act on the result whatever it was. In the light of the past few years that looks like the model for how such things should be done.