Anything you can renew, cancel, track or raise a problem about needs somewhere to live.
Memberships, Bills, Paid Requests and Shop purchases require an account. Piggy Pot contributions and Wishes do not.
The reason
Each of the first four is something you will want to come back to — renew it, cancel it, track its delivery, accept a completed request, or raise a problem. Without an account there is nothing to attach that to, and "email us and we will find it" is a worse experience than signing up.
The card verification step
Once your lifetime spend passes £500.00, a one-off £1.00 card verification is required before further purchases. It confirms the card is yours, and the amount is stated before you pay it.
Guest purchases you have already made
They are still yours. Use Find my purchase with the email you paid with; making an account later does not automatically attach them.