Actually it depends on the processor. Nowadays it's rare, but in the past there used to be software TLBs where a TLB miss did trap into the kernel, and there was no radix tree-like page table structure in the definition of the architecture.

SPARC and MIPS for example worked like this, and server POWER chips had a hashed page table that many OSes populated lazily, effectively treating it like a (more efficient) software TLB.

Well, MIPS is still in widespread use in wifi hardware, and POWER is being resurrected for a scale-up way to deal with a growing database, considering the current generation scales higher at about a similar pricepoint than a 4-socket Intel machine. So I am not sure what the past tense is supposed to mean, if it denotes the architectures to no longer compromise a significant part of world-wide (say DRYSTONE) MIPS, or their lack of use where they are good at (false).

I am not sure about MIPS, but other processors have moved away from either software TLBs or hashed page tables (POWER9 supports tree page tables). Hence the past tense.