Ill agree with you in theory but plywood is not going to distribuate the weight evenly on the carpet. There will still be pressure points where the studs land. Granted the plywood will help distribute the load that piece of carpet will see a constant load as to the rest. Even when you walk or stand you are never in one place for 24/7. Ever seen wear marks in carpet in frequentlytraveled areas? As a suggestion have a carpet guy remove exactly the piece under the hearth (with a carpet knife). Then store it and have it seamed back in when you remove it. That way you will only have the fade and wear issue.