Pence could have (and should have) done that. It would have made it clear that there were legitimate questions. If even a few of the battle ground states had looked into it, it would have been on record and then the courts couldn’t say we had no standing. I understand that Biden would have been selected president, but court review afterwards would have been more feasible.
BTW, “standing” is a dumb reason not to take a case. I understand that I as a resident voter in Texas have “no standing” in objecting to Fetterman’s fake senate election in Pa., but I certainly have standing when there is fraud in Pa. (and Ga. and Az., etc.) for the national presidential election. Their fraud affects my vote even though I am not a resident there.
Every battleground state had an opportunity to do that -- BEFORE January 6th.
I said right here on FR back in 2020 that the most prudent, and urgent, approach for any of those state legislatures to take would be to convene and vote on its own slate of electors -- even an outlandish one for a candidate that couldn't possibly have won the popular vote in that state. The important thing to note is that this would have had to be done before the electors convened in the state capitals for the Electoral College vote on December 14th of 2020.
Once that date had passed and no legislature had taken any action, anything done on January 6th of 2021 was a futile waste of time.
But all of the battleground states, which definitely had the POWER to do as you suggest, had already refused to do so.
Congress has no supervisory authority over the States appointment power.