But there's no evidence that switching to self-paced work samples would cost them less. With Google's popularity, they'd get more false-positives from candidates that copied the code from widely disseminated previous projects. False-positives cost money.
Your medium size firm with smaller volume of candidates won't have that problem of increasing false-positives.
Sure, with whiteboard interviews, the rejected candidates (and even ex-Googlers) can write a "brain dump" blog with blow-by-blow algorithm questions but history seems to show that these don't work so well as cheating mechanisms.
What kind of work sample project could Google realistically design for 10000 programmers to complete? (It can't be as hard as "solve this Clay Millennium problem" or as easy as "reverse this string". Anything between those 2 extremes is trivial to copy to github.) How often do they need to redesign the work sample? What about objective "comparisons" which was touted as a feature of that method? What about the programmers that don't want to do the work sample? (They do exist!) Is there also a cost to filtering them out?
It's great you're really enthusiastic about work samples and want more companies to adopt it but I see no slam dunk evidence that they are the universal best method for every company.