I'm guessing that Binance went with USDT than with USDC simply because USDT has a lot more liquidity compared to USDC.
Trading volume in the last 24 hrs as per CoinGecko:
^Can't expect this to be super accurate but it's clear that USDT has far more volume.
Direct link to check with Stable coins category on Coingecko
If anyone wants to see a comparison of trading volume growth amongst some stablecoins, let's check
From Coingecko's stats, BUSD from Binance is at third position and is a little bit less than USDC. It is a significant achievement for Binance and BUSD if you know other exchanges mostly don't support BUSD. They want to fight seriously against Binance.
It's very hard to get trading pairs for altcoin/ BUSD on non-Binance exchanges.