Good article here about cross-chaining: https://www.roadbikerider.com/latest-rbr-newsletter-2016/227-issue-no-709/2044-to-cross-chain-or-not-to-cross-chain. Couple of excerpts:
cross-chaining on the big/big is the most common cause of a chain getting hung up and not being able to be shifted down off the big cog or chainring. The cause is usually a chain that’s been sized too short.
The other issue you might run into when using the big/big cross-chain position is having the chain fall off the chainring when you shift from the large chainring to the small chainring. This can happen if the front derailleur isn’t perfectly adjusted. It’s more likely to kick the chain off shifting from the big/big because the chain is as far to the inside already since it’s on the largest cog. The chain is also tensioned as tightly as possible when it’s on the big-big.
The combination of the spring tension and chain position makes it much more likely for an out-of-adjustment front derailleur to throw the chain off. The fix is dialing in the front derailleur adjustment. If you can’t do that on the ride, change your shift sequence and shift down onto a smaller rear cog before shifting from the big to small chainring – and you won’t have the chain fall off.
Although the taboo against cross-chaining seems to be diminishing these days (SRAM, for example, seem to think it's fine), it feels like a distressing lack of mechanical sympathy to me, particularly if done deliberately and/or for an extended period.
(A suspicious person might suggest that SRAM might not be inclined to advise people against cross-chaining if it leads to them selling more chains, chainwheels and sprockets to replace ones which have worn out quicker than they otherwise might have done.)
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