The problem is that at some point you'll become the bottleneck and projects will be delayed as a result. Or you'll get sick, a loved on gets sick, etc, etc. Either way productivity will suffer and things generally start to spiral downwards then (people get bored, leave the company, putting more work on you, etc.).

In many places there is always something urgent and there will never be a good time to slow down. Then you end up in my first point eventually. So part of your job is to create that breathing room, push back on projects, get people trained, etc. Think long term and not just moment to moment.

edit: And if you think training people now is painful, doing so when you're actually past the breaking point will be be a lot harder and cause a lot more disruption.