Let me ask you a question. Do you honestly believe that a big part (if not the key part) of the leave campaign (pick any one you like) wasn't about immigration and border control?
I note that I'm afraid you didn't even attempt to answer my extremely straightforward question.
See I'm not a brexiter/leaver/whatever (Personally I think it's a terrible idea), but it's blindingly obvious to me that a lot of leave voters (maybe even the vast majority) thought the main issue was immigration and that Mrs May had a choice either exit the single market, or basically ignore the result of the referendum, she chose the former and not the latter.
Soft brexit (i.e. EEA-like access) plus spend the next 10 years figuring out a better exit deal would have been an option.
UK spent 40 year entangling with the EU, disentangling cleanly in 2 years is a pipe dream.
It is still a possibility though; declaring for hard brexit could very well be a negotiating tactic (as in 'nothing left to lose') as May hinted to the possibility of a transitional agreement.
I entirely agree the 2 year timeline is massively unrealistic (downside to something being written in a treaty agreement with no intention of it ever being excercised)
The challenge for me is that soft-brexit is basically no brexit 'cause EEA access == sign-up to the four fundamental freedoms and accept the primacy of EU law, which seems to cover most of the things that the leave campaign wanted to get rid of.
As you say this could well be a negotiating tactic though, and no-one will really know until they start the negotiations. I think it's entirely possible that once the details are fleshed out people might seek to change it.
Soft brexit would only be a transitional state, with a set timeline or undefined. The hard brexiters would grumble at the former and be completley against the latter though.