Honestly, I think this would have the potential to work. TV shows nowadays can yield some very high-quality work whilst having the story as a TV series rather than a movie works better in the show's favour as it allows you to build up characters, scenarios, etc.
Considering the combined cutscene movies alone from the original trilogy and its DLC content are at least 5 hours in length, there's a lot of potential material to use.
As such, here's some questions for you to answer regarding if the original/classic God of War series actually got a TV show.
1. Would you want to watch it (for starters)?
2. How would you want it to be portrayed? (animated, live-action, etc.)
3. Where would you want the series to start? (Kratos' birth, the beginning of the original game, other...)
4. How much of the content outside the original trilogy (Ascension, Ghost of Sparta, Comics, etc.) would you want to see be adapted?
5. What would you change/add/take away?
6. Anything else you can think of...
Looking forward to hearing your opinions on this.