I think the main reason for 16 2/3 Hz was the motor issue, apparently large universal motors have issues with brush arcing at 50 Hz or more.
25 Hz definitely existed and in some rare instances still exists. Austria has a long-ish electrified narrow-gauge (1000 mm) railway line that was electrified in 1910 using 25 Hz. Originally the power station at Wienerbruck also supplied several villages along the line with electricity, today it's only for the railway itself but still 25 Hz.
For the most part Europe uses three different railway power systems, 15 kV 16.7 Hz in Austria, Germany, Switzerland and Sweden, 1.5 or 3 kV DC in a bunch of countries (France, possibly Belgium, Italy, maybe Spain, the Netherlands, Poland, parts of the Czech Republic etc.) and 25 kV/50 Hz (parts of the Czech Republic, the UK, Hungary, high-speed lines in Spain, etc.). I suspect 50 Hz AC is only common in countries that started late into the electrification process, mostly after WWI. Apparently the first Hungarian electric locos used ridiculously complex electromechanical control systems while the 16 2/3 Hz ones simply used transformers with a bunch of taps (very efficient) and the DC ones used series resistors.
