Many tanks are operated without protein skimmers. Some tanks are operated without either a protein skimmer or an plant/algae filter. But do plant filters "replace" protein skimmers? IMO, no. Its like comparing a horse to a car.
Protein skimmers carry organisms without mechanisms to escape the rising foam out of the tank. IMO this includes many bacteria and cyanobacteria. It also carries up and out particulate like left over food and detritus. It also carries out molecules that are attracted to the surface of the bubble, and this would include organic phospate compounds. Protein skimmers do not directly bind and remove inorganic nutrients. It can improve gas exchange between the water colum and the surrounding atmosphere and so help bring O2 and CO2 levels toward equilibrium.
Plant filters directly bind inorganic and some organic nutrients. Plant filters may capture detritus dependant on wether the algae grown has that characteristics (fine, sediment-trapping filaments). Whether these nutrients are effectively removed is a function of the uptake potential of the plant filter, the frequency of harvest, and the rate organics are released by the filter back to the tank. Plant filters do not directly remove bacteria. Plant filters, used properly, can moderate high CO2 levels (and low pH) and push O2 levels in supersaturation. Used improperly, they can cause dangerously high (8.6+) pH levels.
The main advantage of protein skimmers IMO is that they are easy to understand and the results are realized quickly. A skimmer also can respond quickly to potentially catastrophic events like spawning, sporalation, and bactrial blooms.
Plant filters are more difficult to understand and realize a successful implementation, IMO. IMO many of the benefits are secondary and not seen directly by the aquarist.