This is an older house, and there is nowhere near that many receptacles installed in the living areas. When re-wiring a house, to what extent are you required to "bring it up to code"?
That's a question that keeps getting debated, and although I think every state now uses some version of the
International Residential Code or other (it comes out every three years and it takes some places longer than others to adopt a new edition), the way the enforcing authority interprets it isn't always uniform from one jurisdiction to the next. The general rule is that new work must conform to current code requirements, but repairs (including replacements) do not require that the entire building or structure be brought up to modern code standards.
If you only replace the actual receptacles, technically you need a building (electrical) permit, but you would not be required to bring the entire system up to today's code. Once you get into rewiring the entire house, then IMHO you cross the threshold into full code compliance territory. (And, since I am a licensed building official, albeit laid off a couple of years ago, if you were doing this in my [old] town that's what I would tell you if you were standing at the counter asking the question.
Another issue to consider IF you decide to rewire -- the original wiring will have (I hope) been stapled to the wall studs within 6 or 8 inches of each box, and then approximately 24 inches on center. You can't just disconnect the wires and pull them out of the wall, and you're not supposed to abandon them in place. Catch-22. In general, wholesale rewiring is usually undertaken only as part of a full-scale renovation, when the walls are opened up so you have access.
You can always add a couple of receptacles. Don't mis-read what I wrote:
The NEC doesn't specify any minimum number of receptacles. The requirement is that no point on a baseboard shall be more than 6 feet from a receptacle.
This does NOT say outlets 6 feet on center. It says no point farther than 6 feet from an outlet. In general, for a large wall that's 12 feet on center, not 6 feet. But any chunk of wall 24 inches wide or larger is supposed to have an outlet (because anything that wide could possible have a table and a lamp in front of it).