Performance can 'stagnate' if we use our muscles in the same way - such as on the same bike on a particular loop. It's known that off-road riding on heavier bikes with increased drag improves performance on the road. I've forgotten most of the science behind it, but the benefits are there.
You could argue that using a heavier road bike would give your muscles similar challenges - and there's no reason why heavier bikes can't be fun to ride either - provided they are set up well.
In principal, change is good - and as we all know 'change is as good as a rest'