TeamViewer made remote access feel trivial: install it on both ends and you're driving someone's desktop through almost any firewall, no networking knowledge required. For one-off support that convenience is hard to argue with. The reasons people leave tend to be the same two - cost and trust. Licensing has a reputation for getting expensive and for flagging ordinary personal use as commercial, and the entire session routes through TeamViewer's own relay servers, which is precisely the dependency a security-minded team doesn't want sitting between their admins and their machines.
The open source alternative below takes a different shape: a self-hosted gateway you reach from a plain browser, brokering RDP, VNC, and SSH to the machines behind it. There's no agent to license on every endpoint and no third-party relay in the path - the access server runs on your own infrastructure, so the only thing standing between a user and a remote session is software you host and control.