You'll need to whittle down what you mean by "Plants" vs "animals". Like <PERSON> states do you mean only autotrophs (animals that produce their own food)? Do you mean only animals derived from autorophs (ie an alien venus fly trap) do you mean only organisms that appear plantlike (fungi are not autotrophs). You address that other "animal" life must be simple, so at least the bacterial distinction vs plant is not an issue, so bacterial symbiotic relationships still work even with earth plants. To have this happen you would basically need to make it so that large multi-cellular heterotrophs don't give significant advantage to single celled heterotrophs. Making it so that plants cannot be consumed by heterotrophs as a source for food is one option, there by stunting the available food resources for all heterotrophs.
I believe it is possible for large multi-cellular heterotrophic life to simply not exist. But what you will eventually be left with afterwards is suspect. Plants use CO2 and O2 to live, using the carbon from CO2 as their primary structural material for everything. Producing lots of O2 can result in oxygen poisoning in other life possibly destroying symbiotic relationships with bacteria, or even killing themselves. Likely plants would fight through this, and fires would be far more likely (releasing CO2). Plants would then have another issues.
* Surviving fires
* Getting more CO2
If plants keep encountering fires, plants will either need to incorporate fires into their life cycle (as some modern trees do), or be built to simply survive fires (as some modern trees do). 943
Some conifers actually encourage fires with dry needles in order to kill other plant competition. With this you might have a situation where plants don't even die with the fires, keeping CO2 stuck inside the plants instead of the air, stunting growth of all plants. Plants that have quick life cycles or life cycles that incorporate their own destruction by fire to spread seeds would have the advantage of quick adaptation to the ever changing landscape caused by the atmospheric imbalance of primarily having autotrophs, but plants built to survive from the get go might out-compete these plants by simply not providing enough room for them to exist.
If CO2 is removed from the atmosphere, then plants can't grow. So depending on the decomposition rate and CO2 released that had been sequestered by plant growth, plants may need other strategies in order to get enough carbon to actually live. One way to accomplish this is parasitic activity. Some plants already act as parasites to other plants, normally trees, and derive some of their nutrients from them. Conceivably then, you could even have plants that eat other plants entirely in order to get CO2 or other nutrients, since simply extracting it from the air is not a good long term solution.
Presumably, in such an large animal free planet, you would have a bunch of "plants" that could withstand fires, have quick life cycles to quickly adapt to the changing environmental situation, and plants that essentially kill and take over other plants. This would then cause an arms race for "predator plants" vs prey plants, and this may result in what we would call "animals" all over again, at least on the predator side, and maybe only at the "seed" stage which allows them to move to new locations, or simply let seeds be light/tiny enough to go through the wind. The parasitic/predetory behavior of these other plants would likely make them look more like fungi or sessile cnidarians with similar life styles, as feeding on other structures may give enough energy that autotrophic activity is not necessary.
Conclusion
This planet would probably look like a bunch of tough tree like structures with a web of multi colored mycelium and vines, and "potato eye" parasitic structures covering everything, probably with a haze of a pollen like substance in the air and lots of fires starting . Some of your plants will probably become parasitic or predatory at some point, and stand a high chance of evolving into what you would might call an "animal" at least at some stage in their life. 445