Part 1 of the "Physical Layer Simplified Specification" of SD Cards, Version 8.00 on page 263 (Figure 7-1: SD Memory-Card State Diagram (SPI mode)):
Note: SDUC card, card can stay at busy status and does not reply ready
to host during ACMD41 to let host know SDUC card cannot use SPI mode.
EDIT: ...and thick and underlined on page 262:
SPI Mode is not supported by SDUC cards.
So at least Secure Digital Ultra Capacity (SDUC) cards (that is > 2TB I think) do not have to support SPI.
I experienced the same phenomenon with several SDHC cards as well and try to figure out what's the issue at the moment. In a project about 5 years ago, I also had the problem that with a FatFs library, some cards simply couldn't be used.
In a nutshell: I wouldn't bet on it. Try different cards and also consider using other types of memory.
EDIT, a few days/weeks after: Ok, finally got all of the three SD cards I had from different manufacturers working. I shared the initialization steps here: How to initialize/use SD cards with SPI?