Some apps have hardcoded assumptions about the paths, making those kind of setup harder to achieve (you’ll have to patch the apps or do on-the-fly rewrites).
Then there’s also potential cookie sharing/collision issue. If apps don’t set cookies for specific paths, they may both use same-named cookie and this may cause weird behavior.
And if one of the apps is compromised (e.g. has an XSS issue) it’s a bit less secure with paths than with subdomains.
But don’t let me completely dissuade you - paths are totally valid approach, especially if you group multiple clisely related things together (e.g. Grafana and Prometheus) under the same domain name.
However, if you feel that setting up a new domain name is a lot of effort, I would recommend you investing some time in automating this.