Why do people conduct algo trading for companies but not for themselves?

Time + Scale.

The amount of time it takes to build a working algo is extensive. These things are 500,000 - 3,000,000+ “lines of code”, that take a team significant hours to build, test & optimize. These things aren’t “weekend projects”.

A young “quant” can’t necessarily survive working full time on an algo with no paycheck for a year and a half. Once the algo is built, backtested, forward tested and simul-tested — you then need capital to contribute.

If you build an algo that is optimized for $285m USD in capital and you are a 25-year old quant with -$62k in student loan DEBT with -$11k in credit card DEBT and $122 in his/her checking account, they will have to partner with a larger firm with access to larger capital allocations.