Weld repairs on airliners are common. BUT, there has to be a documented repair procedure. This has to be signed off by the aircraft manufacturer and approved by the governing authority (eg FAA). The procedure would typically state:
What the part is and what damage is to be repaired
What weld process to use, current, voltage, gas, filler metal spec etc.
Weld preparation and inspection .
Weld pre-heat, filler metal preheat and how temps are to be measured and recorded.
Welder qualifications (typically welding a similar test sample which is then cut up and inspected).
Welder qualification renewal (when was he last retested).
Heat treatment (time, temperatures, quenching etc). Reinforcement jigs may be required to prevent deformation during treatment.
Post repair inspections (eg X-ray, or dye penetrant inspection) and dimensional checks - in case the part deformed during heat treatment.
Post repair coating/painting (another whole procedure).
Then there is the paper trail which goes in the aircraft repair logbook:
The part serial number, hours flown and number of take off/landing cycles.
The above weld repair procedure.
Material certificates for the filler material, gas etc.
Pre repair inspection report
Records of pre heat temperatures.
Welder identity, qualification and renewal tests dates.
Heat treatment reports. Copy of the chart from the temp/time recorder on the heat treatment oven.
Post repair inspection report.
All of the above paperwork is subject to getting audited, by the likes of SACAA.
So the welder may be very experienced, fully qualified and have a very good idea how to do the work and what process to use. But he is not qualified to write the repair procedure. Also he is likely not the person responsible for post weld heat treatment, post repair inspection etc.
This has nothing to do with bike repairs. There above costs way more than a replacement frame, never mind the cost of repainting.
Carbon frames are much easier to repair to original strength. It is just difficult to not add extra weight and make the repair look invisible. But this is still a job for skilled/experienced repair guys.