Does anyone really do this to their cooling system?

In your case as the system has been opened and fluid changed that recently ago, you probably don't have to go nutz on a flush. but it should be done, and that pipe plug pulled. As long as you get a good, (not worn out, decent quality brand) 6 POINT!!!! socket on that pipe, plug it shouldn't come out too hard. the worst thing, is to try with a wore out, or cheap, (or any 12 point) socket on it, when breaking it loose. The one on my 74 block came out easily, and this was a Rust belt block since it was new.
Any sediment will settle to the bottom of the water jackets, which is where that pipe plug is.... the point of a flush is to get rid of that sediment that can break free under normal use and plug up heater cores, take out water pump seals or such. by doing what you say, you won't flush that sediment upwards and outwards.
Let gravity help you, by having it flow out that pipe plug opening.