Why are MAX-, AD-, LT- parts (among others) so expensive?
Disclosure: I currently work for one of the manufacturers mentioned, I completed an internship with a second, and I know current and former employees of a third. I can't reveal specifics but I can give some general reasons why ICs have variable costs and prices. I also can't speak about the specific ICs mentioned -- even if I knew why my company's version is priced the way it is and could reveal that information, I couldn't possibly know why other companies priced theirs differently.

There are many reasons -- both technical and non-technical -- why the price of one manufacturer's IC may be significantly higher than another's. Below are some of the major ones. Some or all of these may be true for a particular case, and manufacturers may be in different price positions for different IC types (e.g. op amps, ADCs, voltage regulators, etc.).

Technical Reasons

Fab/Assembly

Every manufacturer has a different fab process (actually many processes), and the process used by a manufacturer may have better performance for a particular application or the process may be more expensive (which of course drives up the cost and price of the final IC).

Even with identical processes and circuitry, though, the materials used in the assembly of the IC can vary in performance and cost. For example, a higher quality mold compound reduces stress on the die and therefore improves performance over temperature...at an increased manufacturing cost. To further reduce stress on the die a polyimide layer may be added. Another material choice that can affect performance and cost is the wire bond material -- for example, it is easier to meet or exceed qualification standards (e.g. temp cycle) with gold wire but gold is more expensive than copper. The added cost of higher quality materials may be important for applications which require long lifetimes, severe temperature swings, etc., but would be an unnecessary expense for shorter term applications with little temperature variation.

Test

Production test also has a large effect on overall cost and quality. Virtually every IC requires some sort of trim (e.g. laser trimming) for at least an internal bandgap voltage reference or oscillator, and possibly for offset reduction, gain correction, etc. Adding additional trims and/or trim bits can improve the performance of the trimmed IC at the cost of increased test time (which is increased test cost). Trim may also require the addition of non-volatile memory, which may require additional data retention tests that also increase the test time. The fab process may even dictate whether trimming is done at wafer probe or final test (i.e. after the die is packaged); wafer probe generally has higher throughput (so it's cheaper) and allows the manufacturer to throw out bad die before spending money packaging it, which of course reduces overall cost of test.

Also, while every IC is tested (at the very least for continuity) overall test coverage can vary. Some applications like defense, automotive, or medical require very low or 0 DPPM, which requires the manufacturer to fully test all electrical parameters (possibly over temperature, which significantly increases test cost). Other applications do not require such low DPPM and the manufacturer may choose not to test in production certain electrical parameters which demonstrated a high \$C_{pk}\$ during characterization, especially if those parameters have a long test time or require more expensive tester equipment. Skipping these tests can result in a significant cost and price reduction with very low but non-zero risk (due to the high \$C_{pk}\$) of passing a die that does not meet the spec, which may be worth it to customers in less critical applications.

Non-technical Reasons

One non-technical factor affecting price is which manufacturer was the first to market. This manufacturer has a temporary monopoly or near monopoly and can command a higher price. This manufacturer may spend less time optimizing their production for lower cost in order to be first to the market. Manufacturers which enter the market later tend to optimize for cost to undercut the manufacturer that was first to market since a customer will not switch to a different manufacturer for an identical or nearly identical IC at the same price. The manufacturer who was first to market may still be able to command a higher price if they have established design wins with large customers who do not wish to qualify a new manufacturer's IC even if the new IC is offered at a lower price.

Also, a manufacturer's prior relationships with major customers and perceived reputation can allow it to charge a higher price. Major customers may be willing to pay extra if they have an established relationship with a manufacturer's support teams and/or if the customer(s) have had quality problems with a different manufacturer in the past.

In short

Ultimately, a manufacturer's price depends on which market it is targeting: some customers are relatively low volume but have very high quality needs and are willing to pay for it (e.g. military, automotive, and medical) whereas other customers have much higher volumes and every penny counts. ICs manufactured for critical applications depend on higher margins to make up for relatively low volume, use better quality materials, have more extensive test coverage, etc. ICs manufactured for less critical but higher volume applications optimize cost to deliver lower priced ICs which make up for the lower margins with much higher volumes.