Why do all English verbs have to start with "to" and German verbs don't? In English we say "to play" but in German we would just say "spielen". why don't we say "zu spielen"? Why don't we do this in German? Is it just a weird grammar thing we do in English?
Maybe it's because the infinitive of German verbs is the root + "-en" ("kochen"), or "-ln"/"-rn" ("lächeln", "meistern"), plus they are written in lowercase, so it's easy to see that they are verbs even without a "zu" before.
But in English you have "smile" (noun), "smile" (verb) - likewise for "cook", "beat", "play" etc. - so you need something to differentiate those words. The suffix mentioned above effectively fulfills that function.
First of all, language is an expression of personality.
You can say "Willst du spielen?", "Hast du Lust zu spielen?", shorter and childish "Willst spielen?" or even "Spielen?". All examples are correct but saying more...revealing the personality of the speaker or his intention.
Well this works in English "Play?", "Do you want to play" or "Would you like playing ...".
English provides "to" and "the" which can be use ubiquitously, makes it an easier and predictable language.
It's not very different -IMO-, just style and intention in spoken language.