There’s no other occasion I can think of where an expression becomes vacuously true by being omitted. If it were conceptually coherent you’d write for(;true;). I guess maybe the reason they made C accept for(;;) but not while() is because while() might confuse a compiler by looking like a function call.
Syntax wise, it doesn't really matter. "for" just happens to be the keyword that allows omitting the condition. "While" effectively means "during which". "For" on the other hand has a significantly more flexible meaning; it seems reasonable to me that the for keyword would be more flexible. Syntax wise, the most explicit thing to have in a language would be a "forever" keyword of some sort.