What about the Files app trick?
iOS can create a PDF from several *images* — select photos in Files, long-press and choose Create PDF. It cannot do the same with existing PDFs, which is the job most people actually have.
The Shortcuts app can be made to do it with a "Combine documents" action, and it works, but building the shortcut takes longer than the merge and it has to be rebuilt on each device.
Neither is a reason to pay a monthly subscription for a merge you do a few times a year.
Doing it on a phone without the data cost
A merge tool that uploads is a poor deal on a phone: a 40 MB scan goes up over mobile data, waits in a queue, and comes back down again. On a weak signal it fails halfway and you start over.
Because this runs on the phone, the only thing downloaded is the page itself, once. After that it works in airplane mode — genuinely useful on a train, and the simplest way to prove the document is not going anywhere.
The practical limit is memory rather than data. iPhones handle large documents well, but Safari will drop a tab that grows too big, so on a very large scanned bundle expect to work in two halves.
If Safari reloads the page mid-merge, the file was too large for the tab. Merge in two batches and then combine the two results.