This is a bad analogy. Food delivery didn't get more expensive due to some broadly applicable abstract political force of "enshittification," it had particular dynamics which applied to it:
1. Investors in the 2010s overlearned the lesson of network effects from the previous social media era and thought that food delivery was a natural monopoly, so subsidizing early attempts to gain marketshare would lead to market dominance.
2. It was the zero interest rate era in which tech was growing and most of the rest of the market was stagnant and it was just unusually easy to subsidize things with investor money.
3. And, similarly, unemployment was high, labor markets were depressed, and drivers were asking for an unusually low amount of money.
4. Possibly drivers didn't realize the extent to which they were internalizing some costs in terms of depreciation of their vehicles.
5. Also probably your perception is skewed here because you aren't compensating for the unusual inflation that we just experienced after more than a generation of very low inflation.
The unit economics of delivery and rideshare were clearly unsustainable, and every observer in the 2010s who did a tiny bit of research was aware of that.
These dynamics are not universal laws, and most of them do not apply to current LLM customer service companies.
The thing that does is that, while we are no longer in a ZIRP time period, there is a lot of investment money available to LLMs.
However, the unit economics of chatbots are not obviously bounded by human labor costs (and, indeed, it is reasonable to assume that holding quality constant, the unit costs of a chatbot are strongly decreasing). We aren't coming out of a low-inflation period into a high-inflation spike (and, possibly, are going to do the reverse). There is no real equivalent to the idea of the driver-centered phenomena of a depressed labor market or illegible cost absorption into the equity of vehicles. I don't think anyone makes the case that specifically chat CS bots are a natural monopoly (though they may for fundamental models).
There are certainly reasons why one may be pessimistic of the viability of customer service chatbots, but I encourage people to think past vapid slogans like "enshittification."