"These children are a bit noisy."
While 子ども can be translated as either plural or singular, in this context it would be unusual to say 子ども in the plural sense. It would be confusing, as it would seem to imply just one child, though not explicitly.
If one considers children in an more general sense, where the specificity and number are not relevant, the following sentences would be fine. Actually, adding たち would sound superfluous and unnatural:
子どもがない女 - A childless woman (woman without a child)
子ども天国（てんごく）- A children's paradise (A child's paradise)
女と子ども - Women and children (woman and child)
In this sentence, however, you are presented with an implied situation where there are numerous children. As you want to be understood not to mean any particular child, adding たち is necessary to clarify that you mean the group. In the same way, if in a group of women, if you were to say この女はうるさい it would be interpreted as 'this woman', rather than 'these women'.
The strange thing is, when speaking of one single child "this child", isn't この子 also more usual than この子ども ?
And I wonder, if written in this way, what "these friends" would be... この友達 (ともだち) or この友達達 (ともだちたち) ? :D
Indeed, この子 is more common in colloquial language than この子ども. この子たち is also used. So, these are equivalent in function to 子ども/子どもたち.
The word 友だちたち does exist and is sometimes used. As it does sound a little odd to most native speakers, however, most opt to use 友人(ゆうじん）or 友人たち when making a distinction between singular and plural. Usually, though, language can be worked so that the noun does not need to be pluralized:
友だちみんなが.... All my friends
友だち一人が.... My friend (one of my friends)