Since your losing those ship construction points as long as you don't have one, waiting wastes resources. I only wait if I'm playing a xenophobic race and the loss would be small anyway.

Wasting is probably a better word than losing. But yes if planet does not have a shipyard assigned to it, it is wasting/losing Ship construction points each round. Even a brand new planet (capital only) has Ship construction points once you build a shipyard.

They are not expensive, but the question is why do we not get one to start? Since it seems like everyone would/should build/buy it first round.

You don't only miss out on potential military production, but, by not rushing  a shipyard and colony ship on your first turn you miss out on potential population growth, and thus raw production.

I usually end up with to many resources anyway. The only one im short on is epitheous pollen. So waiting us not a big issue. Point on colonies though. I play slynn, and always convert my constructor into a shipyard. But when i play krynn, or Yor i build the shipyard first instead if rush buying it. I save the credits for asteroids, mercenaries, and starbase upgrades. In the base production was devided between money, research, and money. Without sliders, and the wheel it is not, now production is calculated as one number. In one sense it is wasted, even though it is more.

I build the shipyard.  I then build a space elevator.  I save my early money for a couple good Mercenaries and use those for exploration,  I play in wide open space galaxies and knowledge of where planets are is key.

If the Mercenary selections available are crud, I will use the shipyard buy as a good plan B.

I'm a glutton for punishment, so I tend to play only on the largest 3 size maps, but about 25% below the "recommended" number of opponents, but at minimally Gifted difficulty.  I also like the Scattered or Loose cluster settings, with Occasional settings for everything.

What that means is that like Erischild above, by far the most important thing for me is to scope out the neighborhood to figure out where I have to plan my expansion.  So getting a colony ship fast is mostly irrelevant, because it's gonna be 30+ (or even 50+) turns before I meet someone else.

I need the money for Mercenaries, because I almost always (unless the selection really stinks) want at least 1 of them. Then save cash to trade for techs.

I'm a cheating save scummer. I tend to replay the first 10 turns or so a half-dozen times to get a decent view of the immediate area, then formulate a plan based on which (if any) habitable planets I find, what the available Mercenaries are gonna be, and tile layouts.

What this boils down to is that having a shipyard right away is not usually very valuable to me. Building slow, low-range colony ships isn't worth it beyond maybe the very first one. Scouts are useless. I can't do any "missions" until I tech up, and I need that tech to make a usable sensor boat.  Basically, it boils down to me wanting a colony ship somewhere shortly after turn 10, and that means I don't usually rush buy anything (and certainly not the colony ship itself).  If I rush buy anything, it will be the Space Elevator for a tile that gets me 2 or 3 bonus levels.

In fact, the primary thing I want a colony ship for in my case is to settle a world and pick the Benevolent bonus, because I want the 150 research point Benevolent skill ASAP. That gets me 2 techs, and I'm on a race to get to Ion Drive as fast as I can.

I think the answer to the question is this:  if you've got lots of neighbor civs, or live in a high-density neighborhood of habitable planets, then a mass colony rush is a huge advantage, and rush buys of the shipyard (and potentially production improvements) make a lot of sense.  If the galaxy is much more sparse, then scouting for positional information is by far the most important thing, and teching up to Ion Drive fast is by far the most advantageous strategy. Pumping out colony ships while you're doing that is mostly irrelevant, so why rush buy anything?

I go for the planet rush as fast as I can, so if my home planet doesn't come with a shipyard (it used to -- why was that taken away) I get one as fast as I can.