One possible inconvenience is that if you use a native SegWit address, you have to either send it first into nested SegWit or legacy address before sending your BTC to an exchange (might change in the future when more exchanges support native SegWit address). Other than that, I don't think there's any other problem.
Have you experienced this before? If yes, what exchange?
I have a native Segwit now with balance, but I haven't tried transferring it to an exchange. I'm still thinking about what to do about it or if it is a good thing to do. Probably there will be a warning if there would be an inconvenience when transferring in a specific exchange or something.