I don't think the question is why use 5e, but is 5e the best fit. Maybe? Maybe not.
I can certainly understand why any company would choose this route. More exposure, larger market, brand name recognition, etc. And as mentioned, the past has shown good and positive results. It is easier to sell a familiar set of rules with a different theme than it is to present a whole new set of complex rules to do essentially the same thing.
Another huge factor we often overlook regarding games like this is how many other people are willing to play if we decide we wanted to for ourselves. An original Stargate the RPG could be phenomenal, innovative, and the best thing ever. But if everyone is still playing D&D for whatever their reasons, its not going to make much of a difference.
That said, I have seen more than a few opinions circulating through various circles that some folks are already tired of 5e D&D. Not an alarming number, but those who've been playing since it came out are ready for something new or different. The timing is ripe for new ideas and alternative experiments while the next wave of new players rotate into the 5e frenzy. If this is how the industry thrives and brings about more innovations, then I would say I am a much bigger fan of this edition despite having little interest in the system.
Circling back to Stargate and Wyvern, it is up to them to make this work. 5e could work for this. But don't just reskin everything and call it a day. Break the mold! Keep something if it works for the setting, but otherwise toss it out. Don't just shoehorn it into the system to make it compatible.
I think fans of the series would rather see Stargate the game, but 5e fans might prefer 5e: the Stargate edition. Your call. Good luck!