If we used only capital letters, it would be extremely difficult to differentiate certain things at times. For example, certain words are written in lowercase because they are not proper. Capitalizing a word changes that word into something proper, thus making it easy to know the difference in what the writing means. We need both cases.
The use of both capital and lowercase letters is important for enhancing the written language and aiding in understanding. Acronyms, names of people and places, dates and titles are all recognized more clearly with the use of both cases of letters. Moving to all capital letters would decrease understanding as well and create difficulties for companies whose logos incorporate lowercases letters. There's no need for a change.
No, capital letters should not be discontinued. The mix of capital and lower-case letters is more aesthetically pleasing than having all capitalized letters. Also, sentences and phrases that are typed entirely in capital letters make it look like the writer is yelling instead of conveying their message in a civilized manner.
No, lower-case letters should not be discontinued. They are easier to read. All caps always looks angry or overly emotional. Lower-case letters convey information in a calmer tone. It would be too distracting to try to read an entire book, for example, that's written only in capital letters. Lower-case letters are more reader-friendly.