The ground is a safety feature. It protects you, not your electronics. For example, a kitchen mixer with a metal housing will have that housing connected to ground so that if there is ever a short inside the mixer that causes the metal housing to become electrified then the breaker will trip instead of people getting electrocuted when they touch the mixer.

The ground does absolutely nothing protect your electronics. Nor does it protect children "sticking a finger or something in the socket". Also, running an extension cord across the house is likely much more of a hazard than an un-grounded outlet.

If you want to address the safety issue and are worried about cost then inquire about having only those outlets you frequently use and/or those cheapest/easiest to do rewired to have a ground. Or just install GFCI outlets. Verify with local codes, but national code allows installation of a GFCI outlet with a unconnected ground. A working GFCI outlet will provide better protection than the ground and will protect against more things (e.g. "sticking a finger or something in the socket").