I have watched Supergirl since its inception, when it started on CBS. It started out as a promising new series (with some forgivable port casting choices, notably Calista Flockhart). But once the show relocated to the CW, and moved to Canada to save production costs, things seem to have gone downhill.
Many of Greg Berlanti's shows have a formula, that principally includes "teams" - Team Flash, Team Arrow, even "Team Supergirl" (counting the DEO). That automatically reduces the reliance on the central character. The team approach exceeds "suspension of disbelief" with such items as Winn being the DEO's "Wesley Crusher" (and apparently the smartest computer whiz on the planet), but also someone that can assemble super-suits together. And James (not Jimmy) Olsen, who instead of being a young, inexperienced geeky kid is now the COO of a worldwide media corporation (and a buff adult too). This gets harder to buy every week.
There are also some ridiculous creative choices by Mr. Berlanti. Brainiac now looks more like a cute member of a blue boy band, not the super villain he was supposed to be. And Mr. Mxyzptlk as a suave British suitor for Kara? Really?!? Even the addition of Superman doesn't look so, sorry, "super".
Then there's the title character of Kara. Instead of growing and becoming a better hero, she seems to devolve into self-pity and "no one can understand what I go through". Mellisa Benoist is a likable enough actress - don't make her a spoiled child. If she is going to take on something called a "world killer", don't you think her cousin might want to help too?
There are too many obvious cost-cutting measures in the post-CBS productions. In each 44-minute episode (1 hour minus commercials), at least half that time is spent talking about the feelings of some secondary character. That means less flying, less fighting, and less CGI production expenses.
So what does work? It was a nice touch when Kara would text Clark for advice and communication. But that hasn't been seen in a long time. Also, Kara needs to be allowed to mature as both a hero and a person (which has not happened yet). The crossovers between Berlanti's universe have been kind of interesting, especially with Flash/Supergirl storylines. But that can get tired really, really fast if they are not careful.
Post-CBS, the series has been on the downslide and may continue if cost savings are the principle concern.