Why didn't the Prophet Muhammad choose to stay alive longer?

I read that prophets/messengers can choose to live as long as they like with permission from God to spread the message, such as prophet Noah. Why didn't he stay alive for maybe another 300 years? This way every soul on earth would probably believe in him as being supported by God. This way the Hadith wouldn't be a clobbered mess like it is today. Why leave so early? If he was so worried about his Ummah why wouldn't he have stayed the next 5000 years to guide everyone? Why not be like prophet Noah who lived up to 950 years? Wouldn't that make Prophet Noah the greatest prophet of all time rather than Muhammad? Living so many life times of difficulty to spread his religion? What's the point in caring about the 'ummah' so much when you could've done a HELL of a lot more? Sahih Bukhari Chapter: 8, Prayers (Salat) Hadith No: 455 Narrated/Authority of Abu Said Al-Khudri The Prophet delivered a sermon and said, **"Allah gave a choice to one of (His) slaves either to choose this world or what is with Him in the Hereafter. He chose the latter." Abu Bakr wept. I said lo myself, "Why is this Sheikh weeping, if Allah gave choice to one (of His) slaves either to choose this world or what is with Him in the Here after and he chose the latter?" And that slave was Allah's Apostle himself.** Abu Bakr knew more than us. The Prophet said, "O Abu Bakr! Don't weep. The Prophet added: Abu- Bakr has favored me much with his property and company. If I were to take a Khalil from mankind I would certainly have taken Abu Bakr but the Islamic brotherhood and friendship is sufficient. Close all the gates in the mosque except that of Abu Bakr. https://books.google.co.uk/books?id=kHFvjpewe5AC&pg=PT89&lpg=PT89&dq=Allah+gave+a+choice+to+one+of+His+slaves+either+to+choose+this+world+or+what+is+with+Him.+That+slave+what+is+with+Allah&source=bl&ots=0NV0L3Ks5n&sig=ACfU3U3lPyiH-RRPJ3I7Z7rqX8JdNtTkeg&hl=en&sa=X&redir_esc=y#v=onepage&q=allah%20gave%20a%20choice&f=false