Yeah, "Bad idea" to run with converter unlocked.
(1) Running with TCC unlocked yields higher oil temps due to converter slippage (this is obvious, as stated prior), and
(2) The 4L60E's oil doesn't flow optimally (trans and cooler circuit) when in 4th and maybe 3rd unless the TCC solenoid is positioned for lockup... or so I read, e.g.,
https://bobistheoilguy.com/forums/threads/towing-in-3rd-or-drive.245366/page-2
On our 1995 K1500 there is a GM sticker on the driver's door / jamb that says something like "Do not tow in D4". The issue in 1995 (and prior years) was, when towing, the ECU would shift the 4L60E into 4th but the conditions for locking the TCC wouldn't be met (I believe due to throttle position being too "open" on account of the tow load), resulting in continued running with the TCC unlocked and attendant heat build-up. There were a LOT of transmission failures in those 1995 and prior trucks when towing for this reason, so the story goes. I believe the problem was mitigated in the 1996 and later OBDII ECU's more capable control algorithms.