I do not beleive i have ever read the Bible cover to cover, and i certainly see no harm in doing it that way; however, if one is seeking to establish (prove) something to be true, then Isaiah 28:9-10
:9 Whom shall HE teach Knowledge? and whom shall HE make to understand Doctrine? them that are weaned from the
milk, and drawn from the breasts.
:10 For precept must be upon precept, precept upon precept; line upon line, line upon line; here a little, there a little.
says one must 'cross reference' (here a little, there a little). Even Paul writes that we should study the scriptiures and 'rightly divide it" (II Tim 2:15).
But even so, I have found many 'nuggets' while just reading the Bible without trying to prove anything. Since the Word of God is the Sword of the Spirit
(Eph 6:17), meaning it is the Spirits to yield, and, since God can give you utterance of what to say at any time (Matt 10:19-20), i liken reading the bible, whether to prove something or just to learn more in general, as 'honing' that sword or making it larger because i have ingested more of the Word into my brain for the Spirit to recall. Even further, since faith comes by hearing, and hearing by the Word of God (Rom 10:17; this means reading the Word also since it is the Voice of God), then the more one reads, the more one learns, and the greater is one's faith, because true faith in GOD is believing in what HE said, not just that HE IS (James 2:19; Heb 11:6)
So, read away, but study also.