This is a common misconception. While onboard DRAM can be used to cache data blocks, its more relevant use-case is to hold the Flash Translation Layer (FTL). This the table that maps ranges of “sectors” as they are presented to the host to the actual NAND packages and blocks they correspond to. If an NVMe SSD doesn’t have onboard DRAM, it can use a small allocation (i.e. tens of MBs) of the host’s system memory to hold the FTL, called a Host Memory Buffer (HMB).
If neither DRAM nor HMB are available (say on a cheap SATA SSD or a USB-attached SSD), the FTL has to be read from the NAND flash itself, and directly updated with no write ordering, coalescing, etc. This is order(s) of magnitude higher latency for the controller than an adjacent DRAM package or the HMB—and on cheaper drives without DRAM this tends to be QLC, which is even worse. Updating the FTL the way has a higher WAF which can lead to a shorter lifespan of the drive if there are small and frequent updates. That’s one reason why DRAM-less drives tend to have a lower endurance rating.
So generally speaking you should seek a SATA SSD with DRAM or a PCIe-attached NVMe SSD for your operating system (and any other storage use-case with small and frequent updates where responsiveness is important). And if the drive is going into a USB enclosure—and you plan to use it for more than slowly-changing and infrequently-accessed bulk storage—it should have DRAM.