Why are the frequencies unevenly spaced on old-style analog radio tuners?

Well?

Because the physical positions displayed measured some linear adjustment of a tuning device, like how far a ferrite slug was inserted into a coil. The actual frequency response to that setting is logarithmic, hence the compressed settings at one end of the dial.

I don’t know how “old time” you mean. However, tuning used to be done either by a ferrite (magnetic) slug in a coil or by a variable capacitor. The capacitors were manufactured in two varieties, linear capacity or linear frequency. The linear capacity version was cheaper but, like the ferrite slug in the coil, gives a non-linear frequency tuning curve. More expensive sets used the linear frequency model that had logarithmically shaped plates to get the linear tuning curve.

Thank you!