The different services should actually give you a choice, what you want to use and not what they want you to use. My local exchange is using P2SH SegWit addresses and Electrum use Bech32 and Ledger use P2SH SegWit addresses. Would it be too complicated to give people a choice between the different formats?
Let the customers decide what they want. Provide the research and information on the two formats and highlight the pros and cons and leave it to the customer to decide.

I understand the need for choice, and I agree with it, but at some point users need to be "pushed" into one direction. From what I've heard, the Bech32 are the most efficient ones in terms of memory use, and are a much better option than P2SH. The only reason most segwit adopters offered the P2SH option first, is because they are compatible with both native segwit and legacy addresses, making them perfect for a transitory period. But in the long run, what you really want is to start using the native segwit addresses (Bech32). For this reason I totally skipped the P2SH, and went straight to the Bech32.
I guess we will start seeing a lot of P2SH first, but in the end, we should all use Bech32. The core wallet apparently gives you a P2SH by default, so this should contribute for people to use that one more often. I would say that if you can, you should go for Bech32, since this might speed up the process.
As for coinbase I'm quite curious as well, and I still don't know if they are already using segwit or not. If they are, they are probably using the P2SH ones.