I usually specialize and grab a lightweight library that does exactly (or something I can hack on) what I need it to. The closest exact replacement I have found to datatables is ExtJS. ExtJS has a pretty large learning overhead as well, but is probably more flexible in terms of functionality in the end and has a much more sane API in the end (with the tradeoff of it being much less easy to reskin).
On the other hand, a lot of JS frameworks have tackled a lot of the problems that I used datatables for except in a much better way. Things such as data storage and retrieval, dom manipulation, smart dom rendering. A lot of times I don't need to reach for one of these libraries anymore because the problem is already handled elegantly enough at the framework level. AngularJS in particular really shines here.
https://github.com/Mottie/tablesorter has multiple sorting using the shift key. I alternate between this and DataTables. The hungarian notation threw me off at first too. Far from insane though.
Here's an example of what you have to do in datatables to get the elements displayed around the table itself styled (such as a search bar, pagination, or table meta information)
So, in order to adjust the styling of DOM elements around the datatable, you need to understand a very specialized form of syntax that one particular property that controls all DOM element layouts accepts as a string. And there's only one example.
To control the structure of whats put in the DOM your are going to need something that looks like a template - so it's never going to be pretty and as soon as you choose any approach to templating it's probably going to upset a lot of people.
I agree that the syntax is a bit on the terse side - but it's not "insane" and at least it is there, logical and documented.
I don't find this a problem at all. What's indeed a problem is that it enforces a wrapper div that you cannot control using this syntax. Furthermore, plugins such as ColVis tend to be inflexible due to that wrapper.
I've been using jqGrid for a couple years now, and have been able to make it do everything I've ever needed. It is full of its own quirks, and probably hasn't been updated in a long time, but it definitely got the job done for me on many occasions.
On the other hand, a lot of JS frameworks have tackled a lot of the problems that I used datatables for except in a much better way. Things such as data storage and retrieval, dom manipulation, smart dom rendering. A lot of times I don't need to reach for one of these libraries anymore because the problem is already handled elegantly enough at the framework level. AngularJS in particular really shines here.