true that Knob and tube systems can be safe. IF the wire is in good condition and has never been tampered with or damaged. You can have an electrician put those wire runs on ground fault breakers and that's pretty easy ( cheap) to do as it doesn't involve opening walls or drilling for new wire runs. a good electrician may also be able to do some resistance checks to look for signs of issues but he can't see the wires so can't make assumptions that its ok. Most electricians would probably advise to re-wire and bring it up to modern safe standards I have personally seen lots of connections that were twisted together , not soldered, wrapped in the old black cloth tape and left inside walls and other hard to find places. the chances are quite high that your house has at least one of them that you can't see.
These are definite fire hazards and I wouldn't jump to conclusions that all is fine.
While the chances that your house is going to catch fire are slim there is that chance and some insurance companies may refuse you insurance while others still will, but may not like it and charge more perhaps.
If I purchased a new to me old house I'd first focus on the mechanicals, water, sewer , electrical, heat etc. They aren't as fun and you won't get the visual satisfaction that you'd get with cosmetic improvements but they are most important to look after.
I love the house. The roof line is gorgeous. Can't estimate the date but we know it's old enough to have K and T and it does have an old looking chimney sticking out of it.
don't let me freak you out about the wiring , but when you have time or if you have an electrician around you could do some consultation. If you see reason to open walls then it's helpful to do electrical at that time. Are the walls insulated?
if you want to run new wires an electrician can usually use long bendable bits and "fish tape" to pull new wires in without doing a lot of damage to your plaster or drywall.
usually old homes with K and T didn't have a very high amperage service. If you want electricity for heat or hot water or to build suites it may not be adequate and to increase the panel size you may need new wires to the pole and that would probably include a new meter base and a larger panel. This can add some cost but it's an upgrade that is often worthwhile in this day and age.
old circuit breakers can stick. If they do and if you get a short, the wires can get red hot inside the walls and start a fire. . Its best not to rely on really old breakers, a new panel might be about 2 to 400 dollars so not the end of the world. If it has screw in glass fuses, they can't stick like the breakers because of their design so they are safer. as long as you don't put pennies in there
if they are glass fuses I'd make sure there aren't any pennies behind the fuses by simply unscrewing each one and checking. You never know what a previous owner might have been up to. , again unlikely but that's an easy thing to check.
also look anywhere you can at the knob and tube wiring and if you do see any places where the wire has been wrapped with tape, or any connections that look like a T that are made outside the electrical boxes then investigate further as that's evidence of someone tampering with them. there should be no breaks or joints in the wires outside electrical boxes.