The other residues have no groups that titrate at reasonable pH values.
Lys 10.4 and Arg ~12 (that is so high that it gets difficult to measure);
Asp and Glu 4.5 4.6. The pH of cytosol is ~6.0-7.4 (unless you drink a lot; or
have love problems), so you need lesss energy to protonate Asp or Glu
than to deprotonate Arg or Lys, and protonation/deprotonation is needed
to 'do something'.
Cys is not basic because at ~9.3 it looses its normal proton, and that is
different from Lys that looses its adopted proton at 10.4. Look this up
in the chapter on Lewis acids and bases.
By the way, a nice explanation of pKa, etcetera, is available at:
web-books