That seems a bit extreme. Plant growth can just slow down or stop and maintain their density. They don't just all start to die. If you are feeding the tank nitrates and other organics are still being produced even if they are being absorbed fast enough that test kits can't detect them. Should the nutrients become so low (the input) the plants can't live then you trim or toss some extra plants.
Also don't forget that when keeping plants for nutrient reduction the plants should be harvested at regular times to fully extract those nutrients from the system. I have to pull out handfuls of water lettuce every week from my tank, those nutrients the plants "locked up" are then totally exported from that system.
No one should think in any way that plants are waterchange replacements. They are just another tool in maintaining systems. It shouldn't be thought of that "oh I have plants, I am going to do less waterchanges". Instead it should be thought of as increasing water quality with the existing plan.
