I'd also thought of getting some waterproof pannier covers, but some experienced tourers I spoke with told me that when they've tried that, if they went through a significant downpour, water would either eventually seep onto/into the bags anyway, or would get in when they removed the covers, so I took their advice and didn't go that route.
I have heard tales of such people, but to me they remain illusive as the Yeti. Toured about 11,000 miles with by Robert Beckman Designs (former partner of Bruce Gordon) non-waterproof panniers with rain covers. Never experienced those problems.
"Seep into" is a questionable phrase. In my experience, water got in from the back, as the waterproof covers, made for the water repellent bags, only covered top, front, and bottom of panniers, to allow for rack panniers were attached. As I previously posted, helped, were worthwhile, but still necessitated some sort of waterproof bags inside panniers for full protection. A bonus for the covers is that if conditions were muddy or otherwise nasty, easier to wash the covers than clean the panniers.
I always wondered if there was some combination of water repellent panniers and waterproof covers that completely kept out pouring rain. If so, interesting, but having switched to waterproof panniers, I will not go back. Putting on and taking off covers is still a nuisance.