> There are quite a few symbiotic relationships in nature.
Yes, of course, but unless such a relationship is already established the odds are very much against a random encounter between different species being mutually beneficial.
The interesting bit around cleaning is the relationships are between individual animals rather than being species wide. Some species of fish for example will mix in removal of parasites with drinking some blood and larger animals eating the cleaners also happens.
https://en.m.wikipedia.org/wiki/False_cleanerfish
These things are incredible. (Or incredibly mean?)
There are several examples where small birds, mammals, fish, or even some invertebrates clean much larger animals. The exchange straightforward, large animal gets clean smaller one eats the parasites, etc. https://en.wikipedia.org/wiki/Cleaning_symbiosis