I'd really like to know if any of the Wonders obsolete. If not, it'll be a tough call for cultural games between a Writing->TGL->Civil Service slingshot (for the huge tech/growth/military boost) or Calendar->Stonehenge.
I question the value of beelining for Civil Service.
Does it provide a tech boost? Sure, but it also requires researching a 3rd level tech too early - before you really have the beaker capacity, meaning you will hit a pretty large dead spot of zero tech advancement along the way while other civs are quickly picking up useful lower level techs like Mining and Archery. It provides a
beaker boost relative to what you'd get pursuing another strategy, but because of the aforementioned effect, it actually sets the civ back in tech for a little while.
Does it provide a growth boost? Yes, but only to cities built next to rivers with improved farms along said rivers and only after a long (at that point in the game) research process to get to Philosophy. If you've only got one city you're planning on putting next to a river, the bonus here is pretty dubious. If you're surrounded by rivers, this strategy becomes much stronger.
Does it provide a military boost? Again yes, but it is a boost that is very difficult to leverage, as pikemen are a primarily defensive unit and pursuing this beeline will likely leave the civ in question with quite mediocre production at the time it gets pikemen. Pikemen are very unlikely to be useful as an offensive unit by the time the beelining civ can actually put them into the field en masse. A pikeman does less damage and costs more than a swordsman - it's only real value is in repelling horsemen.
This beeline may be effective against the AI, but I think it's going to be quite suboptimal against humans and really only a good strategy if you start next to Russia or Greece (and are therefore worried about an early horseman rush) in an area with lots of rivers.