In SP, pre-1.03, I buy 300 crystal at the start, and don't start the population upgrade on the home planet for about 15-30 minutes. I lose out on ~3600-7200 credits from the upgrade being delayed.
In exchange, I spend the 750 credits, 225 metal and 225 crystal on research facilities, ships, and initial planet upgrades, because I colonize faster than I could have had I bought the upgrade. I expand to chokepoints, and sometimes to choke off a neighbor AI. I expand so that I'm not wasting resources putting up defenses on interior worlds. And most importantly, I expand so that my metal/crystal income is higher than if I'd played it a little safer with max credit income.
Is strategic map control, resource dominance, and chokepoint efficiency worth 7200 credits?
How much of a jumpstart on research, ships, and colonization do you get for 750/225/225?
I can only answer that for myself: 7.5 minutes jumpstart on expansion is often a BFD.
At a rate of: .5 metal and .5 crystal / second from the homeworld, 225 means 450 seconds, or 7.5 minutes.
If I take planets 7.5 minutes ahead of an "upgrade-thy-homeplanet-first" player (though this timing cannot be translated 1:1, lets just assume 7.5 as a rough estimate), my resource income will expand that much more quickly. As an example, when I take my first asteroid and complete the first upgrade and extractors, I'll generate 225/225 over 7.5 minutes, plus a little cash. When I have 10 planets 7.5 minutes "early", I have successfully justified leaving the planet upgrade alone by a huge margin, without considering the strategic benefits.
Pre 1.03, resources meant cash. Now cash means resources, so this strategy is weakened. However, I hope you can see that the math of the investment in planet upgrades is not a "simple investment you must make", but a trade off. Trading credits for resources on the macro scale. Trading credits for strategic advantage on the macro scale.
I don't know how you guys play, but my general strategic principle is to have my fleets always working, my empire always expanding, my fleet-cap saturated. By skipping the planet upgrade I find that I can generally keep expanding without pause, whereas when I take upgrades too early I have run into situations where I must wait. In the end, that is all that matters, so: if you can expand without waiting around for resources, AND do the upgrade, good for you.
Some maps will favor one strategy over the other as well. If you know that you'll be ganked by 6 AI locked against you, you know that at some point you'll have to put up fences and expand more slowly. Anticipate that point and do the upgrade to suit the map, IMO.