Glenn
This is not an argument worth having, for several reasons:
First, I agree with you that matching cards is a cheesy way of settling ties, and should not be used for serious championships;
Second: from the R&A entry form for the Amateur championship- "4. The 64 lowest scores over the 36 holes and ties for 64th place will compete in the match play stage of the Championship which will commence on Wednesday 21 June over Royal St George’s and be seeded." So they don't use card matching to cut down the field, only for seeding, and I say that is fine.
I am merely advancing the position that matching cards is a valid way of settling ties, admittedly not the best way, but everybody should know that's the way it is when they enter. If you don't read your entry form, don't show up complaining.