realistically, the Enterprise couldn't catch the Narada and had no hope of fighting it
Why not? Ships in Star Trek are sometimes portrayed as possessing exactly the same maximum speed, thereby allowing for fancy chase scenes - but it is also an oft-mentioned fact of Trek that there are ships much slower than the Starfleet frontline ones. Those include freighters and private yachts; it's only natural if a mining rig is included in that category, too...
There's also some plot logic to the odd fact that military power wasn't brought to bear against the
Narada. Seven starships had previously proven insufficient - so it does stand to reason that the Vulcans wouldn't attempt their own attack with even feebler forces. If the
Narada could stop seven starships from firing on its drill, surely it could stop any Vulcan artillery unit or atmospheric fighter or nearspace corvette from doing the same. It just couldn't stop three lightly armed men it didn't even see.
The same logic could apply to why Earth did not resist, although there I'd blame it all more on reaction time than anything else. If the activation of the drill really was Earth's first warning (and Pike had divulged the codes that would make the ship's approach of Sol invisible), then it's perfectly possible that Earth was going to respond - but Spock got there first, destroying the drill moments before Earth did.
It does take quite a bit of suspension of disbelief, sure. But not quite as much as believing that Starfleet would reward Kirk with captaincy and Captain rank for something that made Starfleet look bad. A medal or ten, sure (Prime Kirk had plenty of those). But a promotion? Only if it served the greater political goal of revamping Starfleet to Pike's liking. Which as such isn't a bad idea. It merely assumes Pike had pull.
Which brings up the interesting related question. Why did Pike jump from Captain to a full Admiral in the time Kirk jumped from Cadet (or Lieutenant) to Captain? That's not Commodore or Rear Admiral braid he's wearing while in the wheelchair. That's the thick flag braid plus three thin ones, denoting four steps of promotion all at once!
Timo Saloniemi