Top 3 posterior teeth will be extracted due to an infection and bone loss. Dentist says that I can leave it as is but aesthetics and speech issues. (?)

Very important. Aesthetics and speech are considerations of varying magnitudes depending on your philosophy regarding these things. Of greater importance is restoring the functionality and stability of the arch in this area. However, if there are no counterparts in the opposite arch then it may be a different story. Very important to maintain the structural integrity of the arch. See a Prosthodontist for options.
Damaging events. Your teeth are designed to work together to help you chew, speak, swallow and smile. If missing teeth are not replaced, a chain of damaging events may occur. See your dentist to replace your missing teeth with appearance and function, without harming your remaining teeth or gum.
Possible issues. Some people function well with little to no teeth. Others falter with the loss of one. You know your body best. That being said, if the teeth are visible in your smile then esthetics are a factor. Where do you do most of your chewing? Are you able to chew only on the other side forever if you lose these teeth? If you must lose these teeth are you able to replace them with implants or a denture? .