I live in a large city, and 2 alleys have closed in the last few years. The nearest alley is now outside the city, or on the south side in the baddest part of town. There have been a couple of boutique alleys opening up - one is a high-class singles place, the other is mostly a kids’ place - both outside the city.
This has happened to me, too. Once I stepped in some spilled water near the refreshments area without noticing, and on my next approach I practically flew into the lane. Went down hard, tripped the foul sensor, I forget where the ball went. Those who witnessed it gave me eight points for the dive, three for the landing. 
After that I made a point of staying in the vicinity of the benches whenever I had my bowling shoes on. I also made a habit of doing a test swipe with my left foot on the approach surface before every throw.
Same for me - and I’m left-handed. I went to two places to purchase a set of bowling shoes and when I told them that I needed a left-handed pair they told me that the only brands they sold were handed-agnostic.
Oh, and to back up c_goat and stealth potato’s falling down stories this happened to me once as well. I had just visited the mens room and had apparently gotten the bottom of one of my shoes wet from, uhh, whatever must have been on the floor in there and underwent a significant face-plant the next time I attempted to roll the ball.
Regarding alley closures:
This 2006 article gives the statistic that the number of centers had a peak of 11,476 in 1962 but number just 5,811 at article time.
Not only are the shoes designed to help the bowler transfer energy to the ball, they are also designed to protect the wooden floor of the approach. Those are expensive to replace!
I used to run a bowling alley. I can attest that street shoes can mess up the approach pretty bad. Black rubber leaves marks, which are sticky and cause the real bowling shoes to stick. The approaches tend to get really dirty, or wet from wearing street shoes, which then becomes a nightmare to clean up…you can’t just mop a wooden approach. Water does a lot of damage and can cause the approach to buckle, which then results in having to sand down the approach. There’s also a liability issue…if your sneaker sticks on the approach and you fall and break your face on the lane, the bowling center could be held liable. By requiring that you have bowling shoes on, it reduces chance that a bowler will be seriously injured.
The bowling alley is there mostly for the leagues that bowl there. They’re held to a strict set of standards and if you go in and mess things up, it can be costly for the bowling center to be compliant to those standards. The ABC (American Bowling Congress) used to enforce these standards through the local bowling associations, but it’s changed names sometime in the past 6 years since the last time I was sanctioned.
We used to charge $1.00 for shoe rental. The last time I took my kids bowling (different bowling alley), they were charging $6.00, which seemed ridiculous.
The rental shoes we had were leather soled on both feet and had slick rubber heels. If you’re an occasional bowler, you can do ok with them. You push off with the heel of your right foot for traction and slide on the left foot when you throw the ball.
You can buy a cheap pair of shoes in the pro-shop for about $25-35 and they’ll have the same type of sole on each shoe also. They’ll be a little more comfortable than rental shoes, as they haven’t been abused and haven’t had thousands of different feet jammed into them. However, I was always told by the pros that the soles were actually worse than the rental shoes.
When I was bowling on multiple leagues and averaging just over 200, I had a pair of Dexter SST-5’s, which have a rubber sole on the right foot and interchangeable soles and heels for the left foot. They attach with something similar to velcro, but a lot better. You could change the sole or heel to adjust to different type of approach conditions.
I bowled on a travel-league which took us to a dozen different bowling centers over the course of the season. Some places had wood approaches, others had synthetic approaches. One place we went had no working air-conditioning so the humidity was high and the approaches were sticky. One place was near a beach and there was sand all over the place. It was the best $120 I ever spent (as a bowler). That was about 12 years ago, so they probably cost more now.
You can get bowling shoes at any decent sporting goods store. Prices for the cheaper ones run somewhere around $19.99-$39.99 with I’m sure much higher priced options out there.