Yes, but as I said it is possible to use a separate ID for entry and exit, so unless they were willing to perform a CCTV trawl then your entire journey could not be assessed. The penalty for this kind of anonymity is paying top fare for entry and exit, so only a very rich tube user could bear the cost. The thing that got people to use Oyster in the first place was 'discounted' prices, as in they bumped the price for a paper ticket when Oyster cards were introduced and kept the old prices for Oyster only journeys. Make of that what you will. Paper tickets are still available as of 2026 last time I checked.
There was a similar data trawl when Boris bikes were introduced, and some of the information gleaned from that was quite hilarious but I can't find a link because it was from the old world and now lost in enshitted search.
IIRC the big push to contactless and Oyster before it is just reducing the cost of handling money. Transit agencies do not really want to be in the business of banking, and physically printing paper tickets and maintaining the machines to accept them properly is a lot more expensive than an RFID reader.
In particular for paper and magnetic strip, you have to keep the reader clean enough to accept reads properly, and the machine also needs to not damage the ticket. This is a non issue with tapping.
There was a similar data trawl when Boris bikes were introduced, and some of the information gleaned from that was quite hilarious but I can't find a link because it was from the old world and now lost in enshitted search.