"Stretched" no, but you are allowed to splice them in some approved way (wirenuts for the smaller wires, split bolts or something else for larger) if they won't reach. This is relatively straight forward unless you have something truly archaic like knob and tube (which would be pretty uncommon in most areas of the country for 1950's construction).

The big question to ask is:

Should I upgrade to a larger service in addition to putting a larger/more modern panel in?

The other important (related) questions that will greatly affect cost are where is the panel and does it have to look pretty when you are done? If the panel is in a basement it will probably be cheaper than if it is currently in a clothing closet.

In fact, it sounds like there is no basement, at all, since you wrote that all the cables come from above. What is probably going to have to happen is that the old circuits will probably have to be intercepted in the attic and spliced in one or more large junction boxes to route new cable to a new service panel. That panel can be indoors or outdoors next to the service entrance (meter). If the meter is not close to the new panel location, a small main panel will have to be installed near the meter.

Existing cables to outlets and lights can stay pretty much as they are, or new cable pulled to include ground conductors. New circuits can be added as well.

As ronnatalie pointed out, it will be an important decision whether to go to a higher larger service enabling you to bring in more power. That entails a new meter with a new meter pan, and new "stuff" to get the power to the meter.

Tell me, why do you want a new panel?