I was always paranoid about exposed steel, but having just bought a 25 years old chromoly Kona as a pub/baby seat bike, I have to say I don’t know why I was so worried. It has plenty of chips, and none have rusted or affected the strength of the bike.
Aesthetically, a bit of touch up paint or matching nail polish wouldn’t go amiss, or at least some clear lacquer to stop the air and moisture getting to the bare metal.
Of course, it is always better to treat them and protect them than leave them to rust, but seemingly not anything to panic about, and there is a strange karma to accepting scars and marks as part of the bike’s patina. Admittedly not a karma that I find it easy to live with on my newer bikes, but the Kona is none the worse for it.
What you do need to be more careful of is long term rot from within if pools of water and dirt collect at the bottom of tubes (particularly around the bb shell/seat tube junction. Definitely get some Weigle’s Framesaver in there.