Script style kind of writing
I most often see this in translated stories and personally consider it as someone writing the script of a manga or anime. It's just not the same without the pictures.
Indicating dialog in the usual fashion, using quotation marks, dialog tagging, paragraph separation, capitalization, and other features of novel convention and standard grammar define the novel. They are written in one of three classes of POV. Writing a novel requires its own bit of work and craftsmanship to produce, and is a learned behavior. Many avocations require a learning curve, The novel is simply another one. Play writing has its own formats.
Outside of school, there are several sites and instructional texts that reveal how to write a play or script, how to write prose or novels, how to write poetry, how to format a proposal, contract, or other form of written communication. All of these can be learned, and all follow their own conventions and formats. You certainly can write a script or play if you want to, and help is available to support your choice.
Ararara Wrote: I've never seen that before, except in a few old books in school (literature class)
Yeah, some novels do use odd (for a lack of a better term) ways of denoting dialogue. Paddy Clarke Ha Ha Ha by Roddy Doyle which I read in school used dashes to open dialogue (but not close it). While it was a deliberate choice so it felt ingrained in the narration, it could be confusing to read in parts because there were some instances where it wasn't obvious when it switched from speech to action tags/ Paddy's inner monologue. It felt a bit alienating until I got used to it, so my advice would be to avoid breaking web novel conventions unless you're specifically writing a script.
That being said it's a very valuable tool for writing the first draft! All my first drafts look similar, except I use speech marks and a basic 'said character' at the end. No action or dialogue tags unless they come naturally, just basic speech. As you said, it feels natural and comfortable because it's a lot easier, which is essential for getting words down on the page. You can always come back and clean it up during the second draft, or shortly before publishing the chapter if you don't write to the end before publishing chapters.
If it's how you feel comfortable writing, I'd say write it out and see how you feel about it. Read it or hand it out to trusted friends and get their feedback on it. Absorb some other writing and arts while you're at it. You'll be able to look at it with a clear head, a new perspective and with help from others.
Not many people would enjoy this format, especially since novels are not written that way, so the traditional style would likely get you more views. But if you don't care about that and still prefer writing your own way, then go for it.
My story uses this format a LOT, and mostly because I don't read enough novels growing up, but I have some experience writing scripts, so I write them in any way I'm happy with. And so far, I'm really loving it as I love writing dialogue and character interactions. I know that it can turn some people off, but I don't see myself as someone who would adapt to a different writing style simply just to get attention. If people like it, neat! If they don't, that's cool.
The last thing I wanna feel is to hate working on something that I'm passionate about. If I don't find joy in it, then what's the point? Not everyone's style is the same, and it ain't hurt to be a little different.
TL;DR: You do you! Nothing's stopping you.
Also, I clicked on the link in your signature, but it leads me to the dashboard. Just replace the dashboard link with your fiction page link. Cheers!