The common expression by all means seems to advocate the use of all means possible in order to accomplish a certain object, when in fact it expresses the use of any means to do it. I realize that all can mean any when used with a negative phrase, such as beyond all hope. Because, of course, if one is beyond any hope, he is also beyond all hope (and vice versa). But in a positive context, such as with by all means, it doesn't necessarily follow that when one uses any means to accomplish a task, that he uses all possible means. Why is all used to mean any in this expression?
To my ear, any means exhorts any one particular method, whereas all means implores the use of all and sundry methods.
Consider these two sentences employing the same structure:
'This machine can be operated by all people.' - thus - 'This task can be completed by all people.'
Here, we mean that any individual would be capable of completing the task.
Does the same not carry then for,
'by all means'
That said, however, it is my understanding that 'by all means' and 'by any means' have different meanings:
'by all means' - a response to a request; 'of course'
'by any means' - to indicate that you will try everything to achieve your goal (aside: here, also note that 'everything' means 'every single thing until one works', not 'all things at once') .