Speedwell - Flower or Weed?

I cut some grass today, which means I must be feeling a lot better. The two-week cold is finally coming to an end as the 14 day mark approaches.
I re-cut everything I did two weeks ago, trying to maintain at least a bit of control!  Then I took the area between the Red House and Betty’s and cut the knee-high grass down to size. (See extra.)  The rest I left because I just don’t have the energy for more than a couple of hours of this physical work.
So these speedwell flowers have survived another day, which is no bad thing as they are very lovely.  On the web they are described as “a common lawn weed” but how can something so lovely be seen as a weed?