Currently the incoming texts pop up on the main screen, they lock up everything you are doing, and if you dismiss them then you may likely forget they have been received.
New emails, leads, and even sales calls come up in the message center on the top right - adding new texts to this section would allow them to be checked in the same manner and cut back on the amount of texts that get 'overlooked' due to user being preoccupied with the person they are currently working on.
In all honesty, there are times when you are entering notes or doing something that requires your full attention and are not able to get to the text the instant they arrive. If you click them then the only way to get to them is make a note of the client(s) or go to the sms received report. Not all agents have the access to the reports so it is not always an option.