Hey, maybe it's not germane to you or others but if Barry and pals are going to keep using the facilities, keep coming up with new gear and use the tech there, then I think that kinda needs an explanation in the show. Where are the resources to do that coming from? Hey, the real explanation is it's a show where they already have that set built and damnit, they are gonna get some use out of it.
But really... The computers, satellite hook ups, and yes the power for things like the holding cells, which they are still using... That should somehow be explained even if it's, "Wells gave you ownership and with that you are now in charge of the funds budgeted to keep STAR operational" or something.
A very simple assumption can be made that explains this. Harrison Wells (and subsequently Eobard Thawne) was an immensely wealthy person that likely poured a lot of money into STAR Labs itself. STAR Labs has likely always had massive budget for its operations thanks to outside funding and various business contracts, but mostly thanks to Wells himself. Assuming ownership of STAR Labs means assuming ownership of all of the company's assets that are to be used for company operations.
If a father dies and leaves his tech company to his son, the son does not simply become the owner of the company's building that is made of brick and steel. He becomes the owner of all of the company's assets, operations, and contracts.
Furthermore, Caitlyn and Cisco are scientists who have been using the tools and resources that have been at their disposal for some time now since Wells was "alive". Cisco also seems to be somewhat of an inventor. Not that it really matters, but the show has given no indication that the team has greatly upgraded the facility or that they've been getting all kinds of new, expensive gear.
Either way, it's important to remember that each episode of this show essentially contains 45 minutes of content. There are many characters, a main plot, and various subplots that need attention each week, along with action sequences. The kind of explanations you're looking for are virtually unnecessary because they don't really affect the storylines or character development, for the most part. For Harrison Wells' lawyer or the characters to go into more detailed explanations of Wells' will or the day-to-day budgetary operations of STAR Labs and how they pay for water and electricity, it would mean losing 30-seconds to a minute of dialogue or screen time for something else in the episode that is likely more essential in pushing the story forward or developing the characters.
This is already a very "talky" show with lots of jargon and characters explaining logistics/science to the audience. I don't really feel it needs to be more talky to appease those who will feel the need to nitpick at things that are ultimately inconsequential. It's not about needing to keep things "light and breezy". It's more about focusing on what's truly important.
And the playing with action figures thing I think is apt. It came to me when they went all those episodes holding those prisoners in the Pipeline. When we were kids you always got the play set with some sort of "jail" to put the bad guys in, but since we're kids we don't think about the logistics of keeping a human being locked up, much less ones with powers. It was enough just that they were " behind bars". And apparently for a nice chunk of the previous season... The writers of the show were in the same mindset because the show never touched on it. Characters in cells for weeks looked exactly as they were when they first arrived. That to me is silly. That's power Rangers level nonsense. I can't go two days without a shower or a shave but these characters were held in cells with no bathroom facilities and no sense of how Barry and friends fed or cared for them in any way. My gut tells me that's why they wrote out the villains they were holding. It was an untenable situation they had written.
I believe you and I discussed this during the last season, but the fact that something isn't explicitly shown in a TV show or movie does not mean it never happens.
Obviously, some suspension of disbelief is required for certain aspects and concepts of this show, but regardless, you seem unwilling to make assumptions about things that occur off-screen or aren't explicitly stated. For instance, a simple assumption can be made that they dropped meals into their cells three times a day and then connected each cell to a container that allowed them to relieve themselves and clean themselves once or twice a day. With the resources of STAR Labs, it's not crazy to imagine that they would have devised a way to take car of those prisoners.
I like the show. I have watched it every week, but these things stick out to me as a weakness in how they approach their world and stories and characters. I am all for "it's just a show just relax" when it comes to a lot of my super hero fiction. I don't think things like magic or super powers all need airtight explanations. This show has already gone "timey-whimey" with it's time travel/timeline stuff and.., that doesn't bother me. But I do think there are aspects in terms of writing for this to be a world that I can buy into without having to just hand wave it as "it's just a show" that have been and continue to be sloppy. Again... I think many fans just give it a pass because "it's fun" and feel somehow such details would detract from that. I think such things would enrich the show, but... Strokes and folks and all that.
I don't think I've really seen anyone give things a pass because "it's just a show" or "it's fun so who cares". It's just that the lack of explanation of certain details, logistics, and intricacies is not something that ultimately hurts the show or hinders it from effectively telling the stories they're trying to tell.
Of course, I welcome more details and more sound logic, but the examples you've given aren't things I view as true weaknesses of the show. If this was a show that was a little more steeped in "realism" and going for a more realistic/real world approach to telling these stories, I think certain details would matter more and some concepts would need to be presented differently.