CSIRO/Data61 have demonstrated with their Zebedee system [1], that the precision mechanical system is optional. Their handheld LIDAR head bounces around randomly and the system is able fit and register the new measurements within the 3D model that it is progressively building.

Such a handheld LIDAR would be a very cool hobby/amateur project, as the mechanical side can be simple and low cost, making the capital cost low. The smarts are in the software and maths. There is also that fascination/aha factor of working though the maths and realising that smart processing means that some "obvious" things, such as precision mechanics, aren't actually necessary, then seeing it work.

[1] https://www.data61.csiro.au/en/Our-expertise/Expertise-Cyber...