And they've been lying this entire time.

Which is why if you think that, you can't just ask them to agree not to have weapons, as you suggest upthread. You have to ask them to also abandon their entire nuclear energy program. Which is one of the reasons they can't get to a deal.

That's the thing with mines. You have to find them as they tend to move around somewhat. The Navy is going to clear a navigation channel wide enough for ships to pass through.

There already is a navigation channel wide enough for ships to pass through, which is why traffic never stopped entirely. The Navy might clear space on the far side of the strait (from Iran) so ships don't have to pass quite as close to the Iranian shore - which isn't really relevant for civilian traffic, but is very relevant if we want to move naval resources through.

And yet, some are going through anyway.

Yes, because they got permission from Iran, which made it feasible for them to go through. Which wouldn't be the case if the limiting risk were mines, rather than shoreline attacks. Which is why clearing the mines won't help civilian tankers transit the strait, because they'll still be vulnerable to missiles and drones. Which were the things that were damaging those ships in the first place, not mines.

The US government is quietly insuring the tankers, btw.

No - they've been offering to insure the tankers - with a facility that started at $20 billion. Which went almost entirely unused. Almost no one took them up on it. They recently doubled that to $40 billion, and it's still the same. Because even if insurance is available, the tanker operators don't want to risk the actual physical threat to their vessels and crew, even if they can get reimbursed.:

Missile and drone attacks, electronic interference, and unpredictable transit conditions continue to shape decision-making, with many shipowners unwilling to expose crews and vessels—even with insurance in place.

The absence of naval escorts has further reinforced that hesitation. While U.S. officials have floated the possibility of military support, no escort program has materialized, leaving commercial vessels to assess the risk environment on their own.

gcaptain.com - U s doubles hormuz insurance backstop to 40b in hopes of luring ships back

They don't want their vessels to get hit with missiles and drones. Unless we clear out the Iranian coast, that won't change - whether we clear mines or not.