The journal rejected my paper but invited me to resubmit after revision. Why not just give me a major revision?

This has indeed become common in recent years (as of 2024). As I see it, the main reason is that options such as reject and suggest resubmission lower a journal's acceptance rate, and a lower acceptance rate can make a journal look more prestigious. They also reduce the number of undecided manuscripts piling up in the journal's system.

For authors, once you have revised, you also have more freedom: you can go back to the same journal or choose another. I generally advise following the suggestions, preparing the revision, and resubmitting. In your cover letter, explain the situation: say that the editor invited you to revise, that you have made substantial changes, and that you have responded to each of the issues raised.

With this statement in the cover letter, the journal will send your revised manuscript to the original editor, and your chance of a positive assessment is higher.

Do it as soon as you can and resubmit quickly, before the editor forgets all about it. Good luck.