Do people in the US tend to pay for individual text messages?
Almost everyone in the UK has an unlimited or close to unlimited texting plan (3000+ texts). Given that everyone's paying for it anyway, the actual revenue gained by someone sending a text is 0. In fact, because a text will use some tiny amount of infrastructure, they'll potentially lose more money the more texts people send.
Most people I know who use whatsapp use it more like an IM client for group messages rather than for one-to-one messaging. As everyone has more or less unlimited texting available to them, nobody uses whatsapp for financial reasons because there's no savings made.
This will only be an issue once people start to realise that they're not using as many texts and demand to pay less. I can't see that happening in the UK.
The PR here is hiding the larger issue. It's not end-users that carriers need to worry about - as you say, most are on near unlimited texting plans, and it's rather unlikely monthly plans will drop in price.
No, the problem is the general rise of IP/push messaging across all sectors. Carriers do make significant amounts of money from direct connection billing and bulk SMS. As more brands develop mobile presences the need to contact customers through SMS versus alternative methods will decrease. Push messaging is considerably cheaper, and from the end user's perspective often less annoying and more convenient.
Fortunately (for the carriers), most operate globally, and certain developing markets offer vast SMS revenue potential, more than the West ever did. India alone is a massive user of SMS, considerably more so than the US (partly due to the lack of regulation: a lot of those SMS messages being sent in India are spam).
"Almost everyone" is basically almost everyone you know. It's difficult to find data on the market share of pay as you go plans in the UK but I'm sure it's a significant portion of the market. These plans typically charge for individual text messages unless you get a special plan or meet some criteria (e.g. top up at least £10 a month).
It's huge. The most recent OFCOM market report reckons just over half of all mobile customers in the UK are on PAYGO. Don't under-estimate the UK pre-pay (PAYGO) market. It's quite easy to, because most people reading this are probably on contract themselves.
Not only is pre-pay half the market in the UK, it's by far the hardest to retain. Pre-pay customers aren't loyal (partly because they're not locked in to contracts, partly because they tend to be price conscious), and because they skew young they tend to be the customers more likely to both a) use SMS, and b) switch to things like WhatsApp.
I find that really surprising because phone service is now just so damn cheap in the UK. After a cashback offer, I'm effectively paying £5 a month for more minutes, texts and data than I can hope to consume. I guess my needs are relatively modest, but so (I imagine) are most non-business customers'.
Pay as you go plans also typically charge a fairly significant amount for mobile data too, though. In fact, on giffgaff (a PAYG-only operator which seems to be insanely popular with young people here in the UK), the most sensible way of paying for mobile data comes bundled with unlimited texts anyway.
I could have an unlimited texting plan if I felt like paying an additional $20-30/month. As I did not feel like it, I used to avoid texting for the most part. Now that iMessage is available, I text freely with other iOS users, and still try to avoid texting for others.