Transactions are not only (actually mainly not) about atomicity. Of course it’s possible to keep data integrity without normalisation, but that means you need to maintain the invariants yourself at application level and a big could result in data inconsistency. Normalisation isn’t there to make integrity possible, it’s there to make (some) non-integrity impossible.

Nobody says you have to have only one view of your data though. You can have a normalised view of your data to write, and another denormalised for fast reads (you usually have to, at scale). Something like event sourcing is another way (which is actually pushing invariants to application level, in a structured way)