I've used a pack liner for years -- took a dunking while canoeing once -- and not one drop of water seeped in. A pack cover would have been completely useless.
To me, it's not so simple as to one being always better than the other. There are different factors to consider:
How do you pack?
Do you frequently need access to the main pack? Or do you place frequently-used items in various outside pockets? If the former, using one big liner will be a hassle. If the latter, then the one big liner method can work beautifully. I line my pack, place most everything inside, then twist it tight (and rubber band if canoeing or doing serious stream crossing). Items like first aid, snacks, camera, etc. are placed in different outside pockets protected by ziploc bags.
What kind of pack do you have?
As stated, packs with multiple pockets will be easier to use with a liner than packs with just one big compartment.
The oft-repeated mantra about a pack getting soaked in pounds of water really applies less and less with modern pack materials. A cotton canvas pack from the '70s will absorb a lot of water... but modern cordura, dyneema, silnylon, etc. will absorb very, very little. Don't forget the water that can collect at the bottom of a pack cover! Sure, many pack covers have drain holes, but somehow, the water never drains out completely for some reason...
But what about durability?
Don't use trashbags. Even the so-called extra heavy duty lawn and leaf bags are only rated 1.1 mil. In contrast, a contractor bag has a 2.0 mil rating -- which is twice as tough! While super big and tough, a 35-gal bag weighs just 2.5oz. Don't forget that a liner is protected inside your pack whereas a pack cover is subject to scratch and abrasion outside!
Given the variation in pack design, pack material, and hiker preference -- both liners and covers will continue to exist side by side. :)