Apparently this year in Banff/Lake Louise was the busiest year ever and that is with paid park passes. Next year with free entrance passes will be busier again but I suspect if you are willing to spend minimal time in the Lake Louise/Banff/Morraine lake area and the immediate Jasper area you would still find it a good experience. There are many smaller unserviced campgrounds, for example, along the Icefields Parkway and it is easier to get space in these since so many parks users are either looking to stay in Banff or Jasper or are looking for serviced sites.
There are no private RV parks in the Canadian National Parks though there are a few outside of the Park gates. As others have said, if you are willing to avoid July and August you should be okay. Having said that, we stayed at Lake Louise campground in September this year (we did not have reservations and did get in) and spent 45 minutes driving around the Lake Louise parking lot looking for a space so we could go hiking. Eventually we gave up and hiked at Bow lake instead so there will be crowds in September in the really popular places.
