Yes but the same can also be said for the GL:
That early in the game, your capital is the only one with decent production.
If you build Cargo ship in capital first, then you run risk of missing the wonder.
If you build Great Library first, it's a long delay for either the capital to finish producing it so that cargo ship can start, or else the cargo ship is going to take a long time to build.
So that doesn't seem like a valid reason as to why GL or HG is better than the other.
The thread has kinda diverged by this point. Really, they're both terrible wonders compared to what you can be doing at that point in the game. One free tech from GL seems pretty big - until you realize that you basically lose out on building settlers at that point, or vastly delay NC. How it's going to go is you beeline writing, and along the way you have time to build 2 scouts, a shrine, and maybe a granary. Then you start building GL. You have no settlers at this point. You finish GL and then you open Philosophy (because you researched Calendar while you were building it). What do we do at Philosophy? National College. So you build that next, because why wouldn't you? That's the whole reason you're doing this in the first place.
Unfortunately, in the 35 turns you spend building GL and NC, you've lost all the good settling spots. Furthermore, even if you didn't, now your satellite cities are 25/15/5ish turns behind where they should be at this point in the game. That's a long time to get all those workers built to get those luxes hooked up to get that happiness up so you can grow population. That's an incredible opportunity cost. You've gotten to the classical era, and an early NC, but it's inferior to having a little bit later NC with 4 solid, growing, productive cities.
HG is even worse, because it requires math. Math is on the tech path to friggin nowhere. Only if you were heading to Civil Service instead of Philosophy first would you ever beat an AI to Math, and that's just sub optimal. You're giving up on libraries and the NC and probably the Oracle and delaying your Writing Guild all for 6 food? That's a very poor trade.
Now, ToA -- that's a different story entirely. If you find an early ruin with Archery, and have a semi productive start, it's almost always worth it to try for it. Beg, steal, borrow, chop, whatever -- ToA is incredibly powerful and pays for itself very quickly at very little lost cost. Yeah, you'll probably not get the shrine up for awhile, and may have to rely on ruins/CS's to get your pantheon going. But you'll have a MUCH stronger civilization later.