Capacitors as current limiters

It occurs to me that the function of the ballast inductance (i.e. the
welder) as a current limiter is to provide a reactive impedance in series
with the load (i.e. the pole transformer).  Has anyone tried using a series
capacitor to do the same? The power factor will be horrid, of course, but it
is the same with inductive ballasting, just of the opposite sign.

A quick calculation shows that capacitance values in the range of 300 to 10
uF would be required to limit the current in the 1 to 50 amp range (from a
240 V line). These would need to be motor RUN caps or PFC caps, of course,
and would be quite expensive if bought new. Surplus is readily available,
and at least it would be potentially a lot lighter weight than an inductor.

There might be problems with interaction with the series inductance of the
transformer, particularly when lightly loaded.