Agree with you totally.
Weeds and grass are unfortunately
more prolific than the cultivated flowers we desire to grow. Just a FACT OF NATURE...
You may consider doing this. (work intensive

)
Dig everything good up.


,,,,,, remove weeds as best you can,,, Till/overturn soil however you are able to. Place a weed barrier type of cloth on top. Cut out openings and plant your desired plants/flowers thru those openings. Cover everything with a layer of wood mulch.
My personal fav are the NON DYED natural type.

Other option which is easier, and less work is like you stated above. Pull weeds and mulch. The weeds will come thru, but removing them is easier. Eventually if you keep plucking the top growth of any plant, they cease to grow.
I mulched around my trees in front of the house. Any unwelcomed growth gets yanked,,,,

it is much easier with the mulch in place.

Third option is to do the weed barrier mat in spring time. Once you have the desired flowers coming up, place mat and cut out openings for them to come thru. Then cover with mulch.
I know from personal experience that the weed barrier mat works. When I put up my fence years ago, I laid down a 2 foot wide strip the whole length. I then covered with crushed stone. No weeds grow under the fence now. (many years now) Everything outside of that 2 foot wide strip grows like as before.
When seeds blow in with the wind, they are not able to reach soil. The shoots that are in the ground from runners are not able to poke thru to surface. Water flows thru mat with no problem.