Tbh even without a price cut for the Switch 1 I still think it'll have stronger post-successor legs than the DS. I'm predicting the Switch 2 to launch at 400$, so even if the OG Switch doesn't get a price cut you could still buy an OG Switch for 100$ less, for a good portion of people that may be the better option as a cheap way to get into the Switch ecosystem. Plus the Switch Lite will be half of the Switch 2's price, while the Switch Lite isn't anywhere near as popular as a regular Switch it could still have solid sales over the next few years as a very cheap alternative.
Compared to the DS, the DSI Xl was only 20$ cheaper than the 3DS once the 3DS quickly got its price cut after launch, anyone with half a brain cell would've rather just spent the extra 20$ for a much more superior system that plays both new 3DS games and old DS games, the price gap likely won't be as small between the Switch 2 & Switch 1. The DS Lite existed for 100$ at the time, but again the price gap wasn't as large as what we may see between the Switch 1 & Switch 2.
However, there also may be a good possibility that Nintendo may limit production of the OG Switch consoles in favor to produce and/or sell more Switch 2 systems. Once Switch 2 releases, clearly Nintendo would much rather push people towards Switch 2 to sell consumers new games and even older Switch 1 games. Like Soundwave said, I fully expect the Switch Lite to stick around for several years as the very budget friendly console, kinda like how the 2DS was to the Switch. Tbh tho I could see the OG Switch getting phased out though and Nintendo may just sell the Oled to encourage people to spend only 50$ more for the Switch 2, and to at least offer an Oled Switch for those who want it if the Switch 2 ends up just going for an LCD display like rumors are suggesting.
A potential good comparision for the Switch's post-successor sales may be the GBA. The GBA was widely successful and the DS launched at 150$ with GBA backwards combatibility while the GBA was 80$ at the time. Despite the DS looking like the far better device with it of course being far more powerful,innovative touch screen, and the ability to play DS & GBA games, the GBA still was selling impressively well even though the DS was already out and it being only 70$ more expensive.
The GBA sold around 7 Million Units between April 2005-March 2006, and an impressive 15 Million between Arpil 2004-March 2005.
Switch 1 may be able to do similar numbers if it's between 100-200$ cheaper than Switch 2.
It's good to take into context tho that the GBA was only 4 years old when the DS finished it's first year, Switch 1 will be around 8 years old which means that the GBA was far less likely to reach saturation than the Switch 1 at its 8th year, so we need to keep that in mind as well.
Gonna be interesting to see how it plays out.