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Definitely more faff, and the same delays will happen with whoever comes next. They aren't going to walk away from you and your offer without a real good reason.
I personally think the unknown is what agitates people the most. So constant communication with them / EA just to let them know you are on it should calm them down.
We had 3 mortgage offers fall through after a month with each. But much like you we were the only offer they had, it was a good one, and we were chain free so despite it all it still made more sense for them to stick with us.
We're with L&C and while our adviser has been great at sourcing options and doing the initial application, the 'case officer' we've been 'upgraded' to seems rather less quick to react. She also forgot to ask for bank statements (?!) adding another week to things. We'll be at 3 weeks by end of week and that's with no valuation : / Presume it's more faff to put back on market, have viewings (assuming agent doesn't go back to next best offer as they could have moved on by now?) and start fresh with someone with a chain than to stick it out with us.