Maybe it’s not everybody, but I’d expect exactly that to be the problem why those systems fail.
These things to my knowledge need to be fair, which usually means nobody can be denied their chance from within the system.
In general I’d also try to figure out how fast students need confirmations about their enrolements. A.k.a. can you accept enrollment attempts and only later come back to the student telling them if they’re successfully enrolled to the course? This “later” doesn’t need to be long, even like minutes or once a minute could allow you to do certain checks less often than per request, potentially even on a separate node, … by splitting writes from reads. It’ll also allow you to better cache/cachebust read heavy parts of the system, which likely will be hit hard as well, especially when they become the success indicators. CQRS in general can be a good step to an event driven system, which allows for a few infrastructure scenarios useful for scaling things independently as needed.
