It's because D&D Beyond only offers the Basic content for free, which excludes most of the stuff you are looking for that can be found in the Players Handbook. You are expected to purchase that additional content here on the site to unlock it in the builder.
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"The mongoose blew out its candle and was asleep in bed before the room went dark." —Llanowar fable
Things like Feats, Archetypes, Backgrounds, and a ton of other stuff that is in the Player Handbook.
When will this stuff be added?
Example - Why is Grappler the only feat? Why is Thief the only Rogue archetype?
It's because D&D Beyond only offers the Basic content for free, which excludes most of the stuff you are looking for that can be found in the Players Handbook. You are expected to purchase that additional content here on the site to unlock it in the builder.
It occurs to me that you have already had an answer in this thread. Anyway, I post here below the official answer:
D&D Beyond can be used for free and contains information from the following "free to use" sources published by Wizards of the Coast: D&D 5th edition SRD, D&D 5th edition Basic Rules, and Elemental Evil Companion.
Content from other sources, such as the Player's Handbook, Dungeon Master's Guide, or Monster Manual, will need to be purchased from the Marketplace or accessed via another user sharing content with you via their Master Tier Subscription.