AzB Gold Member
I think that goes for all sides. My take on the only two possibilities that have a chance to be chosen by a promoter:
Alternate: perceived as more fair and you are guaranteed to see both players at the table
Winner: traditional and thought to be more exciting
A small problem for me with alternate is that I sometimes forget who won the flip/lag.
The choice will remain with the promoter/organizer. Anyone who really wants to influence the choice will need to contact one of those.
At carom billiards the problem of only one player playing in a match is larger. At the "small" games where no cushion is required, the skill level of the champions got to the point where the breaker would often run out the game. In the most impressive case of this, Ludo Dielis ran 400-and-out in his first five matches of a European championship (in the version called 18.2 balkline in English). He then missed after 10 in his next match for 2010 consecutive points with only one miss.
The carom people fixed this by letting the loser of the lag start from a break shot and try to tie, which is called "equal innings". There is also a shootout possibility but some tournament formats can handle tied matches.
Winner of the lag breaks on odd games in alternate breaking (I feel weird having to say that to you )