Whiskers are supposed to be thicker...definitely. Occasionally, a loose (shedding) whisker gets caught when combing their faces with a fine tooth comb and pulls out, but normally, there is no problem. They can look a bit 'wild' but that doesn't bother me.
They are an important item to all animals who have them. Changes in whiskers can indicate some conditions which might require attention...for example, if a kitty has broken whiskers, I take notice.