Alphas only have access to the Venture, and for good reasons: the economy.
Your comparison of “100 out of 500” combat ships doesn’t hold: those are racial hulls to begin with, and many of those have specific, specialist roles. You’d have to compare roles (like mining) with other roles (like scanning), for a direct comparison of numbers of available ships, and divide by race.
Training times are less easy to compare: requirements for a hull often include skills that also affect other hulls (in fact more often than not), meaning those skills are fairly general and beneficial overall. While the basic SP requirement for a hull is a baseline for comparison, the highly needed support skills to benefit from the new hull are always left out. You can indeed put a rookie in a Drake in a week, and he’s likely to lose it in under an hour, or be very frustrated with it because he “forgot” to train the weapon, fitting, drones, and tanking skills.
If you don’t want to commit by going omega, you’ll simply have to accept the line that ccp has drawn for this completely free demo status and be happy with the 20M SP you can toy with (out of a total of nearly 600M SP), while the rest of us pay subs and wrestle our way through all the options of how to play.
There is absolutely no danger of this game becoming just pewpew. Omegas mine their hearts out as well (ships don’t grow on planets). Many are “F1 monkeys” (myself included on occasion) who live in the nullsec lands regions of plenty (well, sort of) and who go out mining as well as blobbing and roflstomping, gate camping, bombing, bashing, expelling, and especially saving their rorqual (or other capital ship) buddies who find themselves in a pickle, etc etc.
Lastly, RMT sweatshops would be happy to fly procurers etc as well, on completely free alpha accounts. Oh yes they would.
Note added in edit: welcome to the forums after five years. There have been so many changes to mining in the past five years that it’s rather a surprise to be hearing from you only now, with a fresh forum alt. It’s also interesting you didn’t mention the Resource Wars, which was a permanent event for mining that was silently phased out (without ccp explanation). A revival of Resource Wars, with adjusted rewards to keep them popular would probably receive support from the (miner) player base.