What you describe is basically what we did. Hell, we've even paid our next 6-months premium in advance even though it doesn't expire until the 10th. The issue is that I can get a current card even with the VIN but not a future card because that policy hasn't yet started. It doesn't yet exist. Nor should it need to because it's unreasonable for Tesla to require 60-days worth of proof of insurance (for a car we don't even yet own, mind you) on a car we're paying cash for.
So I had a single document that showed the new car on the ID card as valid and current but only until the 10th. I had another document showing the had already been renewed for the next 6-month-period but because of us already having renewed it and it not yet being current, it still only showed the other two vehicles. This means we literally didn't have a single document that a bot could scan to confirm basic VIN and date window.
Instead, we had to speak to a human who had the power (not an easy task w/Tesla on a normal day, let alone last day of the quarter) to look at two documents and do the complex math of 1+1=2 when their automated system was only s/u to look for 2... even though 2 was only required for leased or financed transactions. 1 was MORE than enough for cash purchases... but this same system doesn't differentiate between the two types of purchases for proof-of-insurance requirements.
This was a silly and needless exercise in futility that almost cost Tesla one sale for the quarter. I'm not so self-important that I don't realize the fallacy in that statement as they wouldn't have noticed a -1 on their final tally. If you're trying to apply my anecdotal experience to the total then you also need to apply some sort of multiplier of how many others were in a similar boat. That's a much larger number and every minute was clearly priceless for Tesla on Saturday.
Lost time is lost money and their goal at the corporate level should be to fix incidents just like this before they ever happen, for their own profit margins even if they don't care about the customer service aspect.