Tech leads should lead the process, not team leads

I know that these two roles can have different responsibilities in different companies, but after reading around on the web I can see that team leads are mainly about people and process management, while tech lead are mainly about overseeing the technical quality coming out of the team.

I’m a tech lead and also really into Extreme Programming, and I really believe that the technical output of the team is highly affected by the process.

I believe that tech leads should oversee also process, and be the first point of contact of the team with other teams and stakeholders.

Having a team lead doing that is overhead for me, because it just creates an extra layer of communication which is not needed and slows things down.

What do you think?