The idea is these classical languages are already represented in modern ones. Each of them has loaned extensively to at least three of the languages in my list.
That can be tricky, though.
Think about all those words that Esperanto took from a Latin/French source, usually taking into account their presence too in a few other European languages:
kuz(in)o, from French cousin (Latin CONSOBRINUS; Italian cugino, Catalan cosí, etc; English cousin, German Cousin, etc.)
nevo, from French neveu (Latin NEPOT-, Italian nipote, Catalan nebot, Romanian nepot; English nephew, German Neffe, Dutch neef, Swedish nevö, etc.)
manĝi 'to eat', from either French manger or Italian mangiare (Latin MANDUCARE, Catalan menjar, Romanian mânca, etc)
voli 'to want', from either Italian volere or French vouloir (Latin VOLERE, Catalan voler, Romanian vrea; German wollen, Dutch willen, Swedish vilja, etc)
paroli 'to speak', from either Italian parola/parlare or French parole/parler (Latin PARABOLARE, Catalan parlar; English parley, palaver)
preni 'to take', from either French prendre or Italian prendere (Latin PRENDERE, Catalan prendre)
etc.
Now, if we consider Spanish as the representative of the Romance languages, all of the words above would not be candidate anymore, as Spanish has
primo, sobrino, comer, querer, hablar and
tomar/coger instead. Not using Latin or French can be a hard decision to make, since we'd be getting rid of an important source for several languages in Europe (and beyond).
I also find that something is missing without Persian in the list. But at the same time, I'd say the counterbalance is quite good, if we see it like this:
"Latin" : Spanish, English, Russian
"Arabic" : Arabic, Turkish, Hindustani, Indonesian
"Sanskrit" : Hindustani, Tamil, Indonesian
"Chinese" : Mandarin, Japanese, Vietnamese