I manage my site via ssh. I expect not to have my editor killed mid-edit!!! Killing off random processes just because the load on the machine is high is unacceptable, especially when someone's trying to get work done! If your machines are underpowered, upgrade them or migrate sites to machines with more power!
If you really don't intend to be providing ssh access, perhaps you can provide us with a discount? Wait, don't bother. I don't want a provider who doesn't provide ssh access. Make it work or let me know if you don't intend to so I can find a new provider.