Dr. Clark and others say it is beneficial but, I am now wondering how exactly since for most of the history of the church people were illiterate and did not own a Bible.
I actually think Dr. Clark overstates the inaccessibility of Scripture in this regard. I asked him once about B.B. Warfield's collection of evidence for widespread readership in the little article, "The Bible, the Book of Mankind." All his reply was that we know more about history now, but that didn't strike me as much of an answer. For instance, Cyril of Jerusalem expected his catechumens to be able to read, and encouraged them to spend time before the catechetical lectures with one reading out loud to others.
Furthermore, say that the proposition is true that most people have been unable to own or read the Scriptures for themselves. As Rev. Winzer has pointed out, that doesn't mean they couldn't have exposure to God's word, because there were workarounds. Furthermore, historically, has the church flourished where access to Scripture was limited?
Reformation Protestants place great emphasis on being able to read Scripture. This is so well-known it feels redundant to point it out, but involvement in Bible translation characterized the Reformation. The Heidelberg Catechism interprets the Fourth Commandment as requiring the maintenance of schools. An emphasis on literacy is inextricably bound up with Reformed doctrine.
Or say that it's true that most Christians have been unable to read the Scriptures daily. What exactly is the logic to then say, "Therefore, it cannot be a command"? The Reformed have always rejected the notion that a command necessarily implied our ability to keep it. Even if we say that the providentially hindered are so far exempted from the command to search the Scriptures, what's the excuse of people who have been reading since age 5 and who have 20 copies of the Bible?
I would not swallow the line that the feeling that you ought to read the Bible every day is a holdover from evangelicalism. The really rather mainstream Reformed Westminster Confession of Faith asserts that all the people of God are commanded to read and search the Scriptures (WCF I.8). The fact that evangelicalism does something doesn't mean it's bad or wrong or unreformed. Another command of Scripture which is difficult to implement but nonetheless binding is,
Prove all things; hold fast that which is good. Take a look at Psalm 119. Did Christ, the author of the Psalm, expect benefit from exposure to God's law? Consider that Christ himself was taught out of the word morning by morning (Isaiah 50:4), and be encouraged to faithfulness in diligently cultivating a personal acquaintance with the great things of God's law.