We must understand that the context of the question is a commercially successful energy storage system., and 'commercial' is perhaps the most important word here.
The manufacturer has to anticipate the users' needs, to product a product that is usable, cost effective etc etc. Different users have different needs.
Let's take a very extreme user, NASA. It's not practical to replace batteries in service, and satellites are required to have decade lifetimes. This means lifetime is more important than anything else. Satellite LiPos are therefore charged to around 3.92 V, and as a result, exhibit decade lifetimes, even under many charge/discharge cycles per day.
Charging to only 3.92 V gives very low energy density. If a battery had a multi-decade lifetime, it would not be suitable for hand-held tools, phones, laptops where the product lifetime is sub-decade, and there is a premium placed on run time, and purchase price.
Consumer batteries therefore are rated to have a capacity as high as possible, while lasting for a reasonable time. Any student of specifications will recognise that neither 'as high as possible' nor 'reasonable' are specifications. However, locating a 'knee' in a cost/benefit graph, and operating just on the right side of it generally gives a reasonable tradeoff.
In the case of LiPos, there is a fairly hard lifetime/capacity knee at around 4.2 V. Chemists understand the degradation mechanisms of the cell system, and it is voltage sensitive. Any time spent above 4.2 V is very detrimental to the lifetime of the cell. Personally, I lie to my charger that I have LiLo batteries, so it only charges to 4.1 V. Tweaks to the chemistry means that some premium cells these days are rated to 4.3 V.
An important part of the 'commercial' aspect of the system is ease of use. '4.2 V constant voltage' is easy to communicate, to understand, and to implement. Give users too many choices and it will complicate the uptake of the product.
With current, it's more complicated. Again there will a graph of lifetime versus charging current for any particular cell construction, but the knee is not so sharp, and the rated charging current varies by more than an order of magnitude across various cell constructions. Temperature is also a confounding factor, one car manufacturer controls the temperature of their cells when fast charging, and the concensus seems to be that they get much better lifetime than most other car manufacturers who don't.
There is certainly a market where 'fast charge' can be sold at a premium. Whether they achieve this performance by using a more expensive cell construction, or a lower capacity cell, or a more limited cycle lifetime, is up to the manufacturer. However, I don't see any open discussion of the tradeoffs, at least in the commercial market, other than a fairly crude division into 'energy' cells and 'power' cells. I'm sure that sophisticated buyers, like militaries and space companies, would be able to have proper discussions with the manufacturers.
The choice of charging current limit is therefore hypothecated on lifetime. 'If you want a 'standard' lifetime, for this particular cell construction, then you charge at up to xC'.
It may be the case that tapering the charge current down as the voltage increases results in a faster charge while yielding the same cycle lifetime. I don't know if manufacturers have done that experiment. It's certainly open to do the investigation. However, the communication of any successful results would complicate the supply of chargers to the commercial market. It's far clearer to say 'maximum charge rate is 1C', or whatever it is for that particular cell construction, especially as the benefits would be likely to be a small fraction of the differences you get switching between 'energy' and 'power' cells.