It can be relatively inexpensive, but you can also make it expensive.
Inexpensive if you buy discount shoes, clothing and are selective about what races to enter (or just time yourself in time trials on tracks or measured courses, or responsibly bandit races, and avoid race entry fees). You do not need expensive facilities or gear to train.
Expensive if you believe all the marketing and buy expensive shoes, clothing, watches, supplements, massages, periodicals, alter-G treadmills, drugs, travel to exotic races, etc.
Some runners wear $500+ in shoes, clothing, sunglasses, compression socks, hats, etc. just to go out on a 4 mile training run at 12 min mile pace whereas others train virtually naked in old hand me down shoes or even barefoot at sub six minute mile pace.
Running is inexpensive because we have people in countries with low per capita incomes(who have and can afford very little in gear and such and do not have access to courts and facilities) being able train to try to become good runners. Enough of them progress enough so they dominate international distance running.
The simple and inexpensive nature of running make it one of the worlds most competitive sports. You can't say that about cycling, swimming, golf, etc. As an individual sport you do not even need social connections, friends or a team to effectively to train at and practice running.
Running is still simple enough that it is a true competition between individuals. The equipment, extras and gear is secondary and really does not matter much. Despite what shoe companies think, no one really pays too much attention to what spikes and clothing the top runners are wearing.