Grousing to the contrary, I think anyone still playing 5E when the 1D&D core set comes out will switch over sooner rather than later. I'm guessing the PHB wil be the best seller by far, though, and the DMG the worst. The Monster Manual's sales will depend on the art, mostly, I think.
I tend to agree, though I think the speed of the switchover overall will depend heavily on three factors:
1) Does 1D&D offer anything "exciting" over 5E, especially something can't be trivially backported to 5E?
Primarily this applies to DMs, I'd suggest.
2) How significant are the non-class rules changes?
More significant changes will slow changeover as inevitably some people will get bees in bonnets re: specific changes and/or not want to learn new rules.
3) The exact situation with D&D Beyond and 5E/1D&D.
Right now up to 13 million of the estimate 30 million D&D players are on D&D Beyond, and WotC are trying to get as many more people there as possible, as their whole heavily-invested 3D VTT strategy requires it. How Beyond treats 5E and 1D&D will be very determinative on the speed of switchover. There are approaches I can see:
A) Treat 5E as "incompatible" with new features, and require buying new PHB/DMG/MM.
This is the most "hardline" approach. No doubt current functionality will be maintained for 5E, but in order to access new/updated functionality, you'll need to buy a new PHB (and possibly the other books) or have them shared with you. I think this is unlikely but it would definitely both piss people off and segregate 5E players in a way that would likely slow uptake.
B) Treat 5E as "Legacy content" and essentially update rules functionality - but not content - "for free" to 1D&D.
In this scenario, all 5E core stuff becomes "Legacy content" which you have to enable, and the rules, like the way the character sheet calculates unarmed combat, for example, change to the 1D&D. You'd only have access to the 5E versions of races/classes/subclasses (albeit likely with free assignment of the racial ASIs defaulting to or forced "on"). You'd get access to all new tools or functionality, but where D&D rules were invoked, they'd be the 1D&D versions. Rules-text-wise you'd still only have the 5E stuff though I daresay there will be a 1D&D Basic Set that's free.
I think this is pretty likely. It'll piss some people off, but I suspect the people most likely to be annoyed are those who are least likely to be using Beyond anyway, and it provides strong encouragement to change to 1D&D.
C) "Free upgrade" to 1D&D for subscribers.
This would be the most aggressive approach, and it's not entirely out-of-line with Microsoft approaches. In this case, as long as you're on a Master level subscription to D&D and own the 5E PHB/DMG/MM, or content-linked to an account that is, you'd get access to the 1D&D PHB/DMG/MM. If you unsub, you lose access unless you buy them separately of course. This is losing WotC a chunk of cash in the short term, but it does mean that you're making people into extra-loyal subscribers, because they need to keep subscribing for stuff to keep working (which is not currently the case). It would also likely massively speed up transition.
I think this is less likely than B, because the sweet, sweet quarterly returns WotC would get from extra millions of people dropping $150+ on the new PHB/DMG/MM in 2024 to the longer-term lock-in of them having to sub to keep owning the books (buying them would still be an option, but people will take a "well I'd sub anyway!" attitude and not do it). However if the transition goes slower than WotC hopes, especially if the 3D VTT is ready and waiting for delicious microtransactions, I think we might well see C.