Oh, I read that in a Ign article, but I found it now and it has an update saying the deal expired so it was apparently not a permanent price drop. The one in the UK definitely was permanent though, and presumably Europe too, from around 2021.

Those cuts seem to be more related to currency alignments and not due to a marketing strategy as most historic price cuts usually are. The point still remains valid that the Switch hasn’t received these. The industry has been known for its aggressive price cuts as the devices become cheaper to produce and as manufacturers attempt to invigorate console sales at the end of the console’s life. 
Switch as a product has remained an attractive option for consumers throughout its run without that incentive.  

Actually if it was a currency conversion it would have went in the opposite direction. Euro and GBP price would have increased or USD would have decreased. The cuts only being in Euros and GBP when those currencies were losing value to the dollar is actually kinda weird thinking about it now. It might be that Nintendo realised how price sensitive those territories were going to be ahead of time, as its in Europe where PS5 sales really suffer due to the price and spike during any sale. 

From Verge:

“After carefully weighing up a variety of factors, including currency exchange rates in Europe and the upcoming launch of Nintendo Switch – OLED Model, we decided that now was the appropriate time to change the European trade price of Nintendo Switch,” says a Nintendo spokesperson in a statement to The Verge.

Yep, I remember this very well. There was even an article here, about the price cut.

It isn't a price cut. At that time the EUR and GBP were strong compared to the USD. That's why they adjusted the price, no price cut. Of course, once you adjusted the price down you can't really adjust it back up if the said currencies become weaker again against the USD because marekting-wise it would be a very dumb move! Anyway, in the videogames industry the USD is always the only reference currency. Only if the price in USD goes down it will be a real price cut. Everything else in the world doesn't matter, they will always be only price adjustments.

Here's a video of a guy who worked for Nintendo for over 10 years answering if Nintendo really cares about outselling the PS2 for that #1 milestone:
https://youtu.be/OwozQQuDe0E?si=ghPim4ozPYsOL42B

To pretty much summarize like many of us expected, Nintendo doesn't really care. Nintendo is more focused on their short term goals and of course profitability over anything. You have to think the main goal for every individual employee of the company is to complete day to day goals that will overall maximize the profit of their business which is every business's #1 goal, people are too focused on their day to day goals to go out of their way to beat a record when there's no major financial incentive to do so.

We know that Nintendo doesn't care from the simple fact that Furukawa recently told investors that there will be no price cuts for Switch 1, Nintendo will simply sell as many Switch 1 units they can while maximizing profit margins, with no care at all that a price cut would increase the chances to outsell PS2.

Switch won't need any price cut to surpass Ps2
It will be 165 million next year,

Who is gonna be at 165 million next year? Because of Sony I can't tell lol