It seems like way more trouble than it is worth.

SWTOR does this and the results are complicated. What happened is the cash shop stuff is mostly dumped on the in game market for cheap. They use gambling packs though so it's partly a result of whales buying huge numbers of packs and dumping most of the items while they chase one or two rare items. But even the stuff that was only available for direct purchase was usually available for a reasonable number of credits given that all subscribers got a monthly allotment of cartel coins and some players were always just going to buy something to sell for in-game credits. In fact the direct purchase stuff tended to show up reliably precisely because if you wanted to spend your cartel coins on something that would get you a reasonable amount of credits, it was a safer bet than a gambling pack. So when I was playing long term and consistently I barely spent money other than my monthly sub and occasionally some additional coins and I had tons of stuff just for in-game credits including really nice mounts that SE would make more than a million off of.

So in FFXIV, the value of some things would become very low in in-game gil. Dye is an easy guess. People would buy dye to sell it for in-game money or they'd sell the extras when 'all they needed was one dye.' They might end up with more total sales this way or not, hard to say. SWTOR basically added money inflation every time they added content to help the pack buyers make credits selling things on the in-game market.

There actually are a few items in the SE cash shop that are also sold on the market board. I have some Thorne Dynasty Mantelshelves for displaying the stuffed tabletop housing items. They were from a iirc Valentine's event more than a few years back. They cost $5.00 on the mogstation when not on sale. I bought a few when they were cheap and I can't get them to sell. It's $5 in real life and I can't even get 1 million gil for them. If I put them up at 500,000 they'd still take months to sell probably, because they haven't added new housing in a while.

The thing is there are some players with huge amounts of gil, but lots of long term players get into the low millions or 10s of millions and then don't much worry about it. And way more people only want to play for a few months so they never get much in game cash or they buy it. So just buying cash shop items and selling for gil would probably not get you a lot of gil for your cash. It'd be less complicated for them to sell gil directly themselves. I'd have no problem with that, given its limited role in the game, and that it would help support content and other nice things like glamours, and it would make crafting and gathering more and more profitable as more and more money came into the game economy.

But honestly, especially since they don't have a test server, I see no reason to risk it when the model they have is already very good. If it ain't broke, don't fix it.