It's not an issue of weakening the defense/target, but a massive strengthening of the offense.

Aside from the doubling of the target's defense expenses (what, like that's irrelevant or chump change?), I can launch 50 or 100 suits against my target for nothing. At that point, a judge having a bad day is enough for me to become a millionaire. Any system which is so trivially exploitable is a seriously bad idea, and I'm a little surprised Eliezer thinks it's an improvement at all.

(I could try to do this with contingency-fees, but no sane firm would take my 100 frivolous suits on contingency payment and so I couldn't actually do this.)