It is a violation when someone doesn't respect our personal space. This is why we teach kids about personal space from a young age. So why do we let people constantly invade our space by text message? Text is a common and convenient way to communicate. Some people use it to avoid ever having to talk in person or over the phone. When a person sends us a message, it is in our space and our heads. We absolutely have the right to decide when to respond. However, many people feel sending a text warrants an immediate response. So they will send excessive texts to make sure you know that.
If someone were to physically poke you over and over or call repeatedly and leave message after message, you would consider this behavior harassment or stalking. Expecting someone to pause life to immediately respond to you is a sign of an unhealthy relationship. When I send a text, and it takes a while for someone to answer, I respect that person has a life and priorities.
I see this behavior a lot in my two teenagers. They think they need to respond right away and even get anxious about not responding quick enough. It's good to help them understand not everything is urgent, and usually, our best replies are thoughtful, not just reactive.
If you are dealing with a text bandit, recognize that it is your choice when to respond. Try conversing with them about your text boundaries and how you are not always available to answer immediately. If the behavior continues, recognize this as a red flag to reconsider your relationship with this person. If that is not possible, like you share children together, set a time to respond that works on your schedule, or respond to a group of messages in one sitting to clear them off. No one has the right to interject themselves into our lives 24/7.
I know this sounds like we are going back to kindergarten, but just respect other people's space and time.