When switching power companies, the new provider will get in touch with the existing one to let them know that you're moving on. You only have to deal with one party for this process.
Why isn't this process the same with ISPs?
If I understand correctly, its just the billing that changes with a power switch - so, simple.
With ISPs there are actual network configuration changes which need to happen - so, not so simple.
EDIT: Re the billing overlap and the 30 days notice. I have had that many times with work connections when we have changed or cut off services.
Can't say if its right or wrong - but seems very common.