Commencer à does not work

I think the rule is that "à + infinitive" can only be replaced with "y" after verbs that either:

a) also take à before a noun, e.g. penser ("Je pense à mes devoirs")

b) never take a noun object, e.g. arriver.

An example of a) is included in the lesson:

Nous pensons à faire nos devoirs. Nous y pensons.

An example of b) is:

Je n'arrive pas à faire mes devoirs".  Je n'y arrive pas.

Commencer takes a direct noun object ("je commence mes devoirs") so you can't use "y" to replace an infinitive.

Bonjour, i've read this thread of questions a few times and I can't seem to understand why you can't say "J'y commence" since commencer is followed by à.  Which i also see is the case on another site that indicates you use à after commencer to mean to begin to.

Is it just idiomatic that you can't say J'y commence and is an exception or is this related to a rule?  If so i'm not sure I see how that is explained.  Perhaps someone can help me?  Is it because "y" can only replace a thing or object (which may precede a noun, such as "à faire mes devoirs") and not replace just a verb?

Also, the comment by Alan states that commencer takes a direct object which contradicts Cécile's response that indicates it does.  Is Alan's statement incorrect?

Merci

I don't think there's any contradiction between Cécile's reply and mine.

Commencer takes à before a verb, but not before a noun.

Penser takes à before a verb, and also before a noun.

It's this subtle difference that means you can say "j'y pense" but not "j'y commence", even if it's a verb that you're intending to replace.

I tried to explain the rule in my original reply. (It's not explained in the lesson, but you can find it explained this way in some grammar books.)

Oh I see thank you. Very tricky