I work primarily in data analytics. It tends to become noticeable in my experience as soon as you're at a few million records[0] on at least one side of a relationship. Especially as we see more columnar databases in analytics, the row count accounts for more than total data size for this sort of thing.
Due to the type of aggregate queries that typify analytics workloads, almost everything turns into a scan, whether it be of the a table, field, or index. Strings occupy more space on disk, or in RAM, so scanning a whole column or table simply takes longer, because you have to shovel more bytes through the CPU. This doesn't even take into account the relative CPU time to actually do the comparisons.
I've never personally worked with a system that has string keys shorter than 10 [1][2] characters. At that point, regardless of how you pack characters into a register, you're occupying more bits with two strings of character data than you would with two 64-bit integers[3]. This shows through in join time.
[0]: Even modestly sized companies tend to have at least a few tables that get into the millions of records.
[1]: I've heard of systems with shorter string keys
[2]: Most systems with string keys I've encountered have more than 10 characters.
[3]: The vast majority of systems I've seen since the mid-2010s use 64-bit integers for keys for analytics. 32-bit integers seemed to phase out for new systems I've seen since ~2015, but were more common prior to that.
