Why brute force breaks·5 min
The O(N·d) wall
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You have a correct search engine (recall@10 vs exact-NN = 1.0) that's also good (nDCG@10 against humans). So why does every company run a vector database instead of your dozen lines? Cost. Every query scores every document: O(N·d). At a couple hundred docs it's instant. At 100M docs × 768 dims it's ~77 billion multiply-adds per query — hundreds of milliseconds to seconds, per query, on a big machine. That doesn't serve a product.
The numbers
Brute force cost per query
docs N dim d mul-adds/query ~time (1 core)
200 64 13 K < 1 ms ← you, now
1,000,000 384 384 M ~0.3 s
100,000,000 768 77 B minutes
Latency AND memory
It's not just compute — 100M × 768 × 4 bytes = ~300 GB of float32 vectors. You can't even hold them in RAM on one box. Real systems quantize the vectors and skip most of them with an approximate index.