The portable angle grinder that I saw them using on TV looked very effective.
In the hands of a competent workman the risk of damage is minimal.
With a cutting blade this is more a "geared metal saw" than a grinder per se.
Blade size could be selected to be only as large as needed for most locks.
Use of a diamond cutting blade that was as durable as possible would minimise the need for blade changes.
While I suspect that the tool they were using was liable to be as good as most, another one which is very uncommon in this sort of application suggests itself.
A carborundum grit or sapphire or other media air powered cutter could be as capable as desired. These are used in industrial cutting applications for metal up to many times the thickness of the largest padlock.
While this would require a significant air supply, a portable compressor of any desired size could be provided. This may be more expensive to setup than most other options but would provide close to "hot knife through butter" cutting and precision cutting location once established.
A guide could be provided to fit through a padlock hasp so no cutting would happen for any grit that got past the 'target',
A recovery tube with suction could be arranged to recover most of the cutting agent and
A hood that swung over the cutting area to minimise back spray.
All this would take some design and setup - but not excessive compared to the task and, once running it would be very fast.
Note - bolt cutters: Many locks, even quite cheap ones, are hardened. A suitably huge bolt cutter will tackle many hardened locks but the weight and jaw size gets very very large and it would be very impractical for the number of locks involved. - I heard an estimate of 45 tons on the initial bridge alone.