We are a nation of distracted multi-taskers.
Multi-tasking is the act of switching attention between many (often five or more) simultaneously occurring events. It is a bit like speed dating only much, much faster.
Speed reading is the act of skimming written material and "registering" about every fifth word. Your brain interpolates the meaning of the missing content via context, size and shape of missing words and cognitive magic. The reader slows down, i.e. more words are registered, when the results of the interpolation starts to contradict.
Based on this evidence, it seems likely that the human brain can function with very sparse information (one-part-in-five transmitted, just to throw a number out) when the information is holonomic.
Holonomic is defined as "Every piece of information is distributed over the entire structure so that each part of the network contains information of the whole." Definition adapted from Wikipedia
That is, the internal consistencies of the sentence regarding tense, gender, passivity, plurality allow the listener or reader to reliably infer the remainder of the message based on a very small sampling of the content.
Grammar matters when your message matters
Ego demands that our listener to pay complete, rapt attention to us. The reality is that people are addicted to multi-tasking. Also, we transmit in an environment of background noise, with radios and cell phones that have static. Many listeners suffer from hearing loss in some or all of the normal audible range.
Use of standard, proper English ensures that the message you intended to transmit is received with fidelity.
I was blessed with a mother who taught English before becoming Mom. I grew up submerged in proper, grammatically correct English. I was lucky.