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This morning I took a look at the Historic Chess Variants category on CVP, and looking for tested variants using a large number of units per army (not counting shogi variants, or those for more than 2 players), I found 2 such variants (Tamerlane and Duke of Rutland's), neither 10x10, that use 28 pieces per side, albeit without exceeding the arguably desirable 50% ratio of pieces to empty cells. I don't know if either of these games were ever played in clubs or big tournaments at any time, though. 12x8 Courier Chess (and also Courier-Spiel to a lesser extent) lasted in vogue in Germany quite a while, and each used a 50% ratio of pieces to empty cells, with a total of 24 pieces per side. I'd guess these variants didn't largely fall away because they used a large number of pieces and pawns, but rather for other reasons. Maybe the board size and shape being awkward wasn't a big cause, either - presumably quite a few boards of this size were made in Germany (where I noticed elsewhere that 10x8 boards for Janus Chess have been made in modern times, too).

In our chess club in Ottawa there is one unusual (largely red and white) paper board people occasionally use that is wide, because the national & provincial flags are printed in the margins to its 8x8 board. A table in our club is suitable for 6 players normally, but just 4 perhaps when that board is being used.

In my elementary school days there used to be very cheap school sets that were used that featured smaller pieces and boards, and I suppose people could get used to such pieces if they were of better quality, with use of e.g. 12x8 boards that had to have physically slightly smaller squares than we're used to for quality 8x8 boards. A Scrabble game board is 15x15 after all, and clubs with adults have no problem using such for serious events. So, perhaps there is little problem with variants larger than 10x10 in this way, if such boards ever get mass produced due to a suddenly popular variant or two of that board size (as an aside, in the odd search result I've seen some people still ask where they can find 10x10 boards, or even 10x8 ones along with a nice Capablanca Chess set). I may take a fresh look at creating 12x8 variants, even if there's little chance one will ever set the world on fire. I suspect the demise of chess won't be for 100+ years anyway, more or less. :)