Not necessarily. In France SMSes are free for any plan costing more than 2€/month ( which you get as a backup or a kid), but still most people communicate via WhatsApp, Telegram, Facebook Messenger. Even the disaster that is the last one has better UX than SMSes.
I only know one person on WhatsApp without a contract (which all have hundreds of free texts), and the Pay As You Go options I see in the UK go as low as a penny per text.
Most phone plans in the U.S. include unlimited SMS/MMS messages, including prepaid MVNO plans that are very affordable (with entry-level plans under $20/month). Pay-as-you-go plans are an exception, but they are becoming less cost-effective as monthly plans become more competitive.
I think the consumer mindset changes as soon as something is advertised as "unlimited", because you no longer have to think about conserving resources.