There are programs that allow you to draft against a computer.
Forge is a fan-created program that lets you play Magic the Gathering games against an AI opponent. One of the modes you can do so in is Drafting, and after the draft is over, you'll be able to play against the AI drafted decks.
Additionally, there's the website draftsim.com. it also lets you ...
Is there a newer alternative that players have moved to?
Arena; that may not be the answer you want to hear, but it is where the players are.
If you're reasonable at drafting (e.g. a 50% win rate or higher), it's much less than 10k gold per draft because of the gem rewards; 4-3 in a Bo1 draft is 1400 gems, which is close enough to the 1500 gems you need.