Okay, we're back!
When we went to commercial, a Large Cloud of Bad Writing was headed directly for Earth...
Everytime something has happened to or is headed toward Earth, there's no other ships around to address the issue.
(Sorry, this is going to get a little long.)
For my money the most legit example of this comes from ST:TMP, where Enterprise is "the only ship in the quadrant" as V'Ger approaches Earth. For the others:
Take STIII for example: When they stole the Enterprise, where was the ships waiting on the other side of the space doors? One, prototype starship, and that's it? They had enough time to call alert, warm up the Excelsior, and chase after them. Yet: where's the patrol fleets? Spacedock tractor beams?
Partial point to you: it is suspiciously easy to hijack ships from Starfleet. Also (arguably) horrifically out of character for Starfleet officers, but yes, suspiciously easy.
Star Trek VI: Kirk, a convicted assassin has escaped, he's heading for the conference. He starts firing on a Klingon ship. Excelsior joins in. Yet, no other Starfleet ships or Klingon ships respond?
Took place around Khitomer rather than Earth, other ship fired on both him and Excelsior multiple times before they fired back. Not technically an example of the trope... but it is
legitimately quite weird that no other ships seem to be around. Another partial point.
I blacked out most of Nemesis during my subsequent bender, so I'll concede this one on principle.
And that's not counting the whole "Only ship in the sector" BS. Or Starfleeet being braindead enough to send the 1701-A to Nimbus III instead of parking Kirk's ass on another ship. Or shipping out the Enterprise-B with half the damn ship unfinished.
Well, none of those are examples of the Earth trope. But yes, they're all completely legit examples of bad Trek writing, for sure.
Then there's Preston and Riker's super-cloak, which the Romulans seem to take in stride, and nothing ever happens to anyone but Preston
Multiple levels of bizarre in that episode. Frankly my sympathies were with Preston, the TNG Federation was forever signing high-minded treaties that made no practical, moral or strategic sense at all.
So yes, that gives us a pretty good sampling of questionable writing decisions of yore. However, of these, only two (and a half counting ST:TSFS) are actually examples of the Federation leaving Earth near-defenseless. And do they add up to:
Starfleet does not act in anyway that could be called rational ro reasonable.
That's a wormhole too far for me, although movie
Starfleet illogic got worse and worse as the original cast movies went on. Actually, though, most
other stories involving threats to Earth do
show Starfleet attempting to defend Earth in fairly logical fashion: ST:TVH shows the-poor-whale's-V'ger disabling a significant network of ships and stations en route to Earth (yes, the story is still calibrated to leave Kirk the only one who can save the day, but the defenses are there
); Best of Both Worlds features an epic attempted holding action at a neighbouring system (in a famous sequence ripped off far less logically, albeit stylishly, in ST09); First Contact has a large battle over Earth itself; the Breen attack on Earth in DS9 has to penetrate heavy defenses with heavy losses to inflict any damage, and so on.
It is true that a couple of lacklustre efforts do provide precedent for the (as usual, more exaggerated) version of the nuTrek trope. I wouldn't go from there to saying that that is "fairly standard" Trek storytelling. Let's not let the NuTrek, as it were, be the enemy of the good.