Non-fish planted tanks are possible, indeed some enthusiasts run these with great results. There was at least one non-fish entry in last year’s AGA contest. Obviously they’re not to everyone’s taste, most of us entered the planted tank hobby through the fishkeeping aspect first and to have a tank with no fish may appear a little odd.
There are some definite advantages though. Virtually no waste products, thus minimal algae risk (algae’s biggest trigger is ammonia/ammonium). No real filtration required, just some circulation to allow efficient transportation of nutrients. More emphasis on fert dosing is necessary, particularly due to the lack of nitrogen/phosphorous that is normally produced via fish food and waste but these can be easily dosed via KNO3 and KH2PO4. There's no limit on CO2 levels either, ensuring fast growth and limiting algae even furthur.
Dutch style tanks normally have fish, normally just one or two species. The oldest running aquascaping contest, Holland’s NBAT, is judged not only on plant health and composition but also on the health of the fish. The judges actually visit the tank owner’s homes, eliminating any cheating via photo alteration as well as getting a real perspective of one’s hard work.