Unfortunately, that’s not really how things work.
If you don’t want to share resources such as CPU, RAM, Disk I/O, Storage, etc you’ll want a dedicated server. Keeping in mind that you’ll still be sharing the network so depending on where you get a dedicated server that could still potentially cause issues.
Beyond that – a VPS is not a cure-all for resource issues. There are, for example, shared hosting plans that give more CPU, RAM, and I/O on highly available and redundant systems without all of the overhead of running your own daemons like the web server, MySQL, email servers, nameservers, etc.
I recommend a VPS when someone wants more control over the system but not for ‘dedicated’ resources or because a site is busy.
Whether or not someone should be on a VPS has very little to do with the amount of traffic and very much to do with the level of access and control they want. There are certainly sites that are on a VPS and perform terribly due to a low amount of RAM for caching, RAM and CPU usage to operate the VPS itself and the daemons.
It is frustrating that people seem to think a VPS is the solution to every problem. For example just because you have a poor experience with a shared hosting provider does not mean that a VPS is the solution or that you will have that same experience with all shared hosting providers.
I guess it is what it is.