I'm in talks with one of the others on that list because I need Amex support.. but in the UK PayPal also do a tier called "Website Payments Pro". It's not the same as a vanilla PayPal account and includes a merchant account and API for doing card transactions. You have to go through screening to be accepted and I've found them to be very professional and helpful (as in, a far better service than the vanilla PayPal service). Only downside so far for me? No Amex.
I think that's a big part of it, particularly if you're trying for the procurement "loophole" which allows low to mid level employees to authorise spend of up to a certain level without going full a full blown procurement cycle.
A lot of the big firms (in the UK at least) will use Corporate AMEX charge cards (rather than credit cards) for this purpose. If they can't pay on their Corporate AMEX they'll often have to go through a more drawn out process to get the payment made by some other method unless they want to make it on a personal card and then claim it back.
I strongly prefer Amex because the consumer bonus is better for me at least and even more importantly it doesn't take me through the Verified by VISA liability shift/security nightmare.*
* Verified by VISA with my VISA card redirects to a third party domain (not the retailer or my bank) which then asks for DOB and very basic details to set a password (and little more is needed to reset the password). Even if fundamentally secure the user education message of this process is awful. I believe that some card providers make better use and of Verified by VISA mechanisms but not all.
Where possible I will use AMEX for all my personal transactions mainly as I have a longer interest free period on spends making budgeting easier, also while its a pure perception thing the few times I have had the need for a chargeback or had a problem with my card its been resolved in minutes.
Of course as a merchant it's higher fees, has weird conditions attached to it and virtually all AMEX users have another credit card (indeed Amex provide me with a visa card for when I can't use my amex) so there is little benefit to supporting amex.
In my experience, a lot of people who work in large companies who have authorization to spend decent money do. They can often get hold of a Visa or Mastercard instead but it seems to be more hassle to get authorized by a higher-up.
Personally, I have an Amex too and I'm not rich or special but maybe it's different in the UK. I use it because I get a ton of airmiles and Amex never seems to get rejected or stopped for fraud checking purposes.
Almost everywhere I go here in the UK accepts it (petrol station, supermarket, etc.) It tends to be small merchants who don't (local takeaways, particularly.)
