I think that's akin to Len Rum blaming Chippy for Brexit, even though Chippy was always a Remainer (whereas Len was banging the drum for Brexit more than most on here a few years ago before he turned full circle), his reason being that because Chippy voted Conservative in 2015 he was effectively voting for an EU Referendum to be granted as it's what Cameron promised. Personally, I'd blame Len far more because if he was as vocal in real life about wanting Brexit as he was on here then he must've persuaded a fair few mates and family members to vote Leave.
I'm not sure too many people could've foreseen that we'd end up with Johnson and possibly Corbyn as unelected leaders when they cast their vote over 3 years ago - only those with a crystal ball could've predicted that. In any case, we've had unelected leaders previously, unless your issue is with who those unelected leaders are. In which case, I'd agree on that as I'm not keen on either and that's an understatement. You could equally blame all those Labour and Conservative members who voted for Corbyn and Johnson as leader of their respective parties. Also, I'n not sure too many expected Corbyn to last this long anyway.
It could also be argued that we might not have had any unelected leaders during this process, let alone 2 (remember May was unelected as well) or 3 (if Corbyn gets in as caretaker PM), if Cameron hadn't been such a shithouse in the wake of the Referendum result and had stayed on to help negotiate our exit.
It's unfair to put the blame for the current political shambles at the door of those who voted to Leave, as parliament itself has completely and utterly failed so far in it's duty to get a deal through, despite having ample opportunity to do so and even though there was one on the table.
Those to blame for this mess are those wankers in government and opposition, not Joe Public.