The primary reason is that most sellers are also buying another house at the same time, so they tend to have more rigid timelines that make your suggestion impractical.
Beyond that, if you go too high on your initial price a lot of people won't look at your property. Most people have a fairly strict price range they are looking for so anything higher will get filtered out. Even if it is within budget but it seems unreasonably high, many people will just avoid it assuming that you as a seller will be unreasonable in general. The price reductions might draw some eyes back to the listing, but price reductions can be viewed unfavorably as well.
If your property is listed for too long, people start to assume there is something wrong with it. It's known as a stale listing and many people warn against buying them.
Those reasons aside, if you don't have timing constraints then you could certainly fish for the highest price. A lot of the strategy will depend on your home and your local housing market, if you're in a high demand neighborhood where homes don't go up for sale very frequently this could work out very well. Consult some professionals, do your own research on your market, and try to remain objective.
A popular approach in my area is for the listings to have an offer deadline, so for 1-2 weekends the seller can collect offers and then decide on the best one. Not suitable for all situations, but in a hot market it works nicely.