You’re inferring that. It doesn’t specify it in the spell description and the rules for Willing state clearly that it’s a DM determination.
Charmed does not make a person Willing either. It just give advantage on the check where a creature is Indifferent. Even Charmed won’t make an Unwilling creature Willing. The rules are pretty specific. Not even 5th level Dominate Person makes someone Willing.
Ah, you finally took a look at the rules. Even if the best you can do is repeat what I said way earlier, it's at least something.
But it is concerning the Influence Action, not the Suggestion spell. I also never said that it would be the charm effect that creates the willingness. I said that the charm effect is already by itself a change in thinking which you claimed wouldn't occur.
But the Suggestion spell creates the willingness and aligns the creature's desires with the urging. The Suggestion has to be a course of action, described in no more than 25 words, and achievable. "Be willing to the spells I cast on you" fulfills all these requirements because, of course, creating one's own willingness is a course of action, it is less than 25 words, achievable, and doesn't obviously deal damage to the target or its allies. Mental activities like thinking are actions and it says nothing in the spell that the course of action is limited to physical activity. And the charmed target pursues the suggestion to the best of its ability. The suggestion could equally be "like me", "love me", "be my friend", or anything else along those lines and per the spell's description, the creature would do its best to like me, love me, or be my friend. And nothing would change if I added a qualifier as in "like me willingly".
Thus, your only way out here would be to say that the target couldn't make himself willing, thus that the course of action would be unachievable. It would be nonsense because, of course, is that possible as phenomena like autosuggestion illustrate, but that would at least be something founded in the rules.
Anyway, I’ve used the word Willing far many times for one thread and I’m Unwilling to keep going tonight.
Have fun.
Be my guest, cheers, and good night!