“All you have to do is read a lot.” as opposed to “All you have to do is to read a lot.”
(Much of the following references OED and Jespersen's "A Modern English Grammar on Historical Principles.")
The "to" (and its loss) is a vestige of Old English that had grammatical cases in which nouns had suffixes indicating both the dative and the form of the infinitive.
History:—As well as the simple infinitive, or verbal substantive ending in -an (Middle English -en, -e), Old English had a dative form of the same infinitive or a closely-related noun ending in -anne, -enne. In Middle English this reduced successively to -ene, -en, and then, -e, and thus eventually became the same as the simple infinitive and reduced to the uninflected verb-stem.
As an invented example:
Help (verb) would have been helpan.
In Middle English, this reduced to “help”.
A/the help (noun) would have had a dative form helpanne/ helpenne
In Middle English the dative noun became -> helpene -> helpen-> helpe->help.
The infinitive and the noun were indistinguishable.
This dative form, which implied to or for {noun}, was governed by the preposition tó/to. Originally, to before the dative infinitive (e.g. to helpan (v.)) had the same meaning and use as before ordinary substantives (e.g. to the helpan (n.)), i.e. it expressed motion, direction, inclination, purpose, etc., toward the act or condition expressed by the infinitive; as in ‘he came to help (i.e. to the help of) his friends’, ‘he went to [the] stay there’, ‘he prepared to [the] depart (i.e. for departure)’, ‘it tends to [the] melt’, ‘he proceeded to speak [the speech]’, ‘looking to receive [the reception[of]] something’.
But in process of time this obvious sense of the preposition 'to' became weakened and generalized, so that tó finally became the ordinary link expressing any prepositional relation in which an infinitive stands to a preceding verb, adjective, or substantive.
The result of the above is that the "to" of the infinitive is now seen as part of the verb, and more a "particle" than a preposition.