If we are to follow usual conventions of English grammar, the preposition "to" should not be omitted. The reason is as following ...
He has {to go to school}.
He has {going to school as a necessity}.
He has {necessity of going to school}.
i.e., He has {complex noun}.
His responsibility is {to go to school}.
His responsibility is {going to school}.
i.e., His responsibility is {complex noun}.
By complex noun, I meant either
- a simple noun with or without adjectival modifiers
His responsibility is {a new school).
- prepositional phrase
His responsibility is {of the school)
- relative wh-clause (what, who, where, etc
His responsibility is {which girl he likes}
- infinitive phrase
His responsibility is {to go to school}
- present-participle/gerund phrase
His responsibility is {going to school)
- coupled predicate
His responsibility is {that going to school is enjoyable)
- modified complex noun
His responsibility is {largely that of going to school is enjoyable)
Therefore, saying
The best thing to do is {concentrate on something}
is akin to saying
His responsibility is {go to school}
which is a poorly written sentence because {go to school} does not fit as a complex noun phrase. It is a verb-phrase.
If you wish to drop the preposition, you would need to turn it into a gerund phrase
The best thing to do is {concentrating on something}
The phenomenon of dropping the preposition of an infinitive phrase is a misjudgment practiced by iphone/android-texting kids, and often overlooked by their grammatical guardians when the verb in the infinitive phrase is longer than two syllables.