From a theoretical point of view (let's leave apart for a moment interpretation and writing), are ties necessary to account for note values that notes and dotted notes cannot provide?
Two tied eighths can be written as a quarter, here the tie is unnecessary.
If each eighth is in a different bar, then we can change time signature (remember, interpretation doesn't matter here) as to put them together, and then write as a quarter, so again unnecessary.
If five eighths are tied, that cannot be written as any dotted note. Is it here where it is necessary? Any other situations?
Update: "Ties" only in the sense of altering note values, phrasing is a different use of them.