Notation is a very crude graphic approximation to rhythm at the best of times and counting and metronomes are even cruder. Western notation and its centuries of hidebound tradition have created the persistent illusion that rhythm is a simple property of notation, when in fact most felt rhythms of any interest are very complex and cannot be notated at all. Having said that, if all you are playing is classical music, which hangs on notation anyway, and counting and metronomes help, then use them, but only as a crutch, a learning tool, until the complete rhythm is firmly in your mind.
There is also a clear difference between feeling rhythm and being able to keep a regular beat; the latter is a very tiny subset of the former. I would be inclined not to worry about bending rhythms in traditional romantic music. Most of it would sound pretty trotty played metronomically wouldn't it ? Metronomic stride and swing, for example a Midi file, sounds okay, but even there, I get the feeling something is missing after a while, something which is vitally present in a solo by Waller, Morton and others.
Rhythm to me lies at the core of music and like music itself, is ineffable in the sense that just when I think I understand a lot, it surprises and delights and tells me I understand very little. I rather enjoy this ongoing process.