We load end-of-day transaction files from multiple banks using the same package. We have multiple SQL Agent jobs and use the /config parameter to provide a different config file for each bank. Package has no problems executing in parallel.
As I said if you only have one SQL Agent job there is a problem, as you have many there is not a problem
As for non-power users managing the jobs, that's done from a web-page that calls sp_start_job. The app pool identity of the site has the permissions required to manage the jobs.
I would call building a web app 'custom plumbing'
Anyway I don't think we disagree here. When we get down to specifics every solution has it's advantages and disadvantages.