Yes you can, but nobody does, because the inconvenience outweighs the advantages of increased privacy.
Cash is doomed by the same problem - it's inconvenient, and also pretty insane to carry around paper tokens when we could carry digital ones.
Even if you do manage to evade some tracking (e.g. by using cash) cameras are tracking you everywhere, we have facial recognition improving rapidly, car number plate tracking etc etc. At some point it will be possible to track your entire life with ease simply from following your movements, and it will be very difficult to circumvent without laws to control that sort of information.
I do think it's more important to control the use of extensive personal information and tracking than to try to limit it, because limiting it simply won't work, and can be easily bypassed.