Well, would a major reboot be worth it, or would it be better to alter the premise? For example, the gate system has them stepping onto unknown alien worlds, but they can always just step back through the gate. So the writers have to give them a reason to either explore (find allies, technology, etc) or a reason they can't immediately leave via the gate they just came through (Damaged DHD's, etc). They also have to always arrive where the gate happens to be, and never know much about what lies beyond the gate's immediate area.
You could give each planet an in-gate and an out-gate and a reason why they can't be in close proximity (like a transmitting and receiving antenna on a radio repeater), and then each visit would inherently require some amount of cross-planet journeying. Unfortunately, a tweak that major would probably mean you'd need to tweak a whole lot of other things so that the show doesn't just look like a screwed up version of Stargate, like Wormhole Extreme.
You could mix premises of Stargate and ship-based shows, and instead of gating between planets, the gates take you to orbiting stations around the planets (which actually makes more technological sense, since geology would bury all the gates but high orbits last virtually forever). Each station would have to have a few shuttles on board (otherwise they'd have been useless), so the shuttles can be destroyed pretty frequently without creating the ST Voyager problem. It also eliminates the long travel times between planets that Star Trek had to occassionally comment on, along with the "assume standard orbit" type dialog that always ate up screen time.
Since the orbital stations were built in large numbers, they would look similar to each other (saving on set production), yet could've been modified by subsequent occupants or visitors (giving an excuse for visual variety and changes required by particular episodes, while explaining why the changes are mostly cosmetic - also saving production costs per episode). That would also allow many or most episodes to encounter aliens on an orbiting station instead of a planet, reducing the need for location shoots, yet always having a planet there if a story requires it.
The system of travel also means that the aliens on a station might often be different from the aliens on a particular planet, creating conflict and drama if the episode is a planetside scavenger hunt, and giving an in-built reason to find lots of aliens playing gods over more primitive planetary populations.
It's also logical that many stations that are still in operation (or were reoccupied) would've put a local gate on the nearby planet's surface (normally either not done or lost to geological processes), so a shuttle trip wouldn't be necessary for most episodes (Star Trek used transporters so they didn't have to keep burning screen time on shuttle arrivals and departures), and yet could be a feature of other episodes, without burning screen time explaining why the transporter won't work on a particular planet because of <technobabble>.
Since the stations are pretty standard and obviously built to monitor the planets they orbit, the whole "scan for ships/scan for lifesigns" can be dispensed with as needed, and a long-term history of each planet could often be recorded on the station, so the writers would have more versatility in revealing an episode's backstory.
ETA: (So for many episodes, the SGC briefing room scenes or ST ready-room scenes could move onto the station itself, with the station's records filling the role of a character).
Toss in Lonemagpie's Timegate
idea, and perhaps some of the stations are locked to particularly critical points of a planet's history, giving a reason why episode after episode is unusually important to the characters in it, as opposed to yet another meaningless arrival of people at the planet's bus station.