I think maybe it's an apples to oranges thing, in this case, from language to the other.
English is a very figurative language. We often describe things as completely different things, for example when you want someone to leave a job or something...
"You should leave that sinking ship!"
Being native in English will help you understand that statement immediately, but as an example my wife speaks English quite well but it's pretty rough around the edges, mostly the basic stuff (she's Japanese) and if I said that to her she would be utterly confused.
We do this often in English and I've noticed over time I'm running in to these situations where I'm often just letting these types of statements roll out, and then I have to either explain to her what I meant or just avoid using these types of phrases altogether.
As a result of being a very figurative language, it would actually seem quite fitting that our filler word of choice would be a word such as "like", it's as if you are constantly predisposed to set up a comparison, or a way to alternatively explain something in a 2ndary way. Let's put it in to a realistic context that it would typically be used "improperly" and as a filler.
"I hate that food, like, I can't even eat it without gagging"
Ignoring that these phrases are often grammatically incorrect from a written standpoint, if you actually consider the placement of the word in the spoken phrase, you can see that it's actually sort of preparation for an example of something. Something meant to elaborate on the aforementioned thought. You hate a food. How much do you hate it? So much you can't eat it without gagging. It's like that.
Japanese does not really have this. Trying to speak like this in Japanese is confusing, while it's not unheard of to make a comparisons in speech to make a point, it's not nearly at the level we do it in English.
That being said I think "sa" is only a Tokyo thing, but I wouldn't argue that it maybe closer to "like" than "eto" or "ano". The thing is that "sa" is also used as sort of a lazy ambiguous "meh" as well (sorts).