I unlocked the Fate Gacha, but...

It seems like it might depend on whether your goal is point accumulation or long-term play. If there's a character you want, I think it's okay to pull. When you set a desired character, only that character will appear. As stated in the [Details], there's a pity system at 70 pulls. Besides characters, you can get diamonds (never seen one), red orbs, green orbs, witch's letters, witch's crystals, etc. For reference, I'm planning to play long-term, so I'm saving up (waiting for a character I want).

If you're not doing it for the points, Mowano is strong even at SR rarity, so I recommend it!

If there's a character you want, the Fate Summon is better than the Pickup Summon. In the current gacha, Mowano is strong even as an SR. If you're pulling from the permanent banner, aim for Lunarin and Natasha, who have low rates, or the practical Florence. However, if you don't have a specific character you want, there's no need to pull. If you're pulling for red orbs and don't have a desired character, it's best to go for Florence and aim for LR5. Also, the pity is 70 pulls, but the rate increases by about 7% from 57 pulls, so you'll get a character around 60-65 pulls. The expected value is around 36 pulls, so the diamond cost is almost the same as the pickup banner. Therefore, it's more cost-effective to pull from the Fate Summon than the Pickup Summon.