There are a few noticeable problems here.
1. You're assuming gathering shards/crystals is anything like gathering crafting mats. Shards and Crystals are stackable to at 9999, maybe more, each. For that to happen with a raw material like electrum, that would require filling up one's entire inventory and that's it. Not only that, but you can't use Wards on normal crafting materials. You have to use King's Yield, and that is not only more expensive GP-wise, but also only works on a single attempt, making it economically not worth it.
2. You're assuming that the dev team doesn't care about botting. First of all, the dev team are players of the game just like anyone else and play fairly just like everyone else. Second, bots are prohibited by the ToS. If they weren't prohibited, everyone would be using bots. The fact that they are prohibited by the ToS and little is being done about it is less attributed to sub prices (as I am absolutely certain that the players who do bot make up less than 1% of the subscription base, which isn't worth defending.) So here's a question: Why prohibit bots in the ToS if the dev team ultimately doesn't care? That makes no sense and it sounds extremely jaded and cynical of the entire process.
3. My "gripe" is backed up with the solution of selling shards and crystals from beast tribe vendors, which renders them completely worthless to sell on the market boards except for convenience purposes. So no, they would not keep shard prices lower. At least not universally. If I want shards, I want to be able to buy them for 10 gil each at a beast tribe vendor. Crystals? 100 gil sounds fair for those. Clusters wouldn't be sold as they aren't nearly as farmable.
4. Your whole argument seems to be defending botters from an economic standpoint. There are a lot of bots, true, but their numbers nowhere near compare to the number of legitimate players. Why else would there be so much action taken against them? Your argument makes no sense.
5. As for new gatherers, I can guarantee that all of the legitimate gatherers want to level their gatherers ASAP. Farming shards and crystals is not at all the fastest way of doing that. Shards are always Level 1. That means maybe 10XP yield with each gathering attempt, maybe more. With how XP scales, this is not at all lucrative unless you plan on botting while doing other things. Crystals only appear at specific nodes in an area and are Level 30, making them even less lucrative for leveling unless botting. I started mining with a crafting mentality. Mine up all of the ore so I don't have to buy it on the market boards. That was my goal. And you know what? I achieved it. Now I'm mining up Darksteel and doing stuff with it. And I am sure there are miners that try to make a profit from mining, and that they do succeed through legitimate methods. But the fact of the matter is that no legitimate player would ever mine up shards and crystals exclusively to turn a profit. Ever.