This makes you wonder what the UK government has been doing for the past 2+ years apart from twiddling their thumbs.
Far as I can tell, the most accurate answer seems to be "trying to preserve the current political parties, probably foolishly so".
My current understanding is that David Cameron did a big mistake by proposing the 2016 referendum. So-called "Eurosceptcism" in the UK is a big if rather questionable force in the Conservative Party and he hoped to give it a venue of expression by way of the referendum, only to have them fall in line afterwards. Obviously, that was a serious miscalculation which led to the need for his stepping down from politics altogether.
I call that a mistake, but this may be an unfair judgement. There are significant indications that he may have had no better option. It may well be that the UK does in fact need to go through a significant period of Brexit-themed reality shock. There is, I have learned, a proud isolationistic passion in much of the British media pushing for Brexit, and many people give it far more ear than it could ever deserve. It is not in Theresa May's power to decree that the ERG and other foolish groups should learn better, and it certainly wasn't in David Cameron's power either. Ultimately, it takes the publish awareness of the British to keep such voices in their place.
The 2016 referendum was deeply flawed from conception, seeing how it failed to address necessary matters of adherence to customs union in Ireland and to the European Single Market. That may have been a deliberate, calculated if ultimately naive choice. Cameron seems to have decided to bet on the power of a simple, nuanceless referendum - albeit one of deliberately ambiguous legal power - to alleviate political pressure over him. He was clearly overly optimistic. Had the vote gone the other way, there would be no need to address the practical significance of a Brexit. But it did not, and the need is real, grave, and badly addressed to this day.
Regardless of superficial appearances and official standings, the actual main issue actually being discussed since 2016 has little to do with Brexit proper. Some people have genuine interest in discussing the necessary technical and legal matters, but they are too ineffectual. I am not sure on whether the main reason is a lack of public support or whether the fault lies in the self-preservation needs of the Conservative and Labour Parties.
Either way, both Parties are in an impossible situation. Conservative needs to seek a way of preserving party unity while at the same time dealing with the utterly irresponsible and opportunistic ERG, meaning that they are prisoners of their own ambition, caught in a loop of nurturing impossible hopes and seeing them destroyed by the reality of facts time and again. Labour is stuck with Jeremy Corbyn, who is in some ways just as stubborn and unrealistic as the ERG despite being head of a largely reasonable representation. It seems to me that the current impasse is mainly a direct result of hoping to solve among the MPs a problem that is ultimately created outside of its scope. There is only so much that they can do while given impossible expectations and utterly inadequate tools.
Theresa May can't make it so that the EU needs to give even further concessions to the UK. Jeremy Corbyn can't make it so that the general public has better awareness of the true consequences of a Brexit, mainly because he seems to be in denial himself. Most MPs are essentially powerless, because worries about breaking up their fragile parties have raised too high. No one can make Brexit constructive in and of itself, since it amounts to feeding commercial and political relationships with hubris where maturity is called for.
It may very well be (and is IMO the most likely future at this pont) that there will be a No Deal Brexit, quite possibly this March 29th still. The postponement is by no means a given, since there are 26 or even 27 chances of forbidding it entirely. Even if it is conceded, there is little hope of solving much of relevance if the only significant change is a bit more of time. Ultimately, the House of Commons is its own main adversary, and needs quite a bit of public awareness and support to break its own impasse. There is no clear path towards that necessary change that does not involve swallowing the bitter pill of actually going through Brexit and earning the disastrous results.