Jesus is the Lord of the Sabbath so he is not under obligation to conform to what the Jews thought was allowable.

Also, for the man to be healed he needed to demonstrate faith in Jesus' authority. The man undoubtedly knew that he was not supposed to carry his mat according to the Jew's law, and so by doing so he demonstrated his faith to Jesus above the Jew's law.

This was why Jesus asked him, to give him the opportunity to display his faith, which is what actually healed him. How many times does Jesus say "It is your faith that has healed you."

Jesus did not just point his finger at the man and heal him, not at all. He made him express his desire to be healed and then made him demonstrate his faith.

When Jesus says "Sin no more, so that nothing worse happens to you." he indicated that the mans sickness was due to his sin, this sin was cancelled (and his illness cured) by his practical display of faith in Jesus.

This is what we need to do if we want to be healed (physically and spiritually), carry out Jesus' instructions even though they seem physically impossible to us and even if they contravene the so-called law. 

Jesus also shows us here of what he thinks of the Jew's rules and regulations regarding the Sabbath. 

I think, to some extent, we all need signs and wonders to believe in Jesus, not necessarily outward healings or transformations but wonders within ourselves or others.

Jesus came to save sinners, and sinners arn't renowned for their faith as we are too engrossed in worldly pleasures. So of course all sinners need something however small to kindle their faith.

It is easy to claim to have faith in Jesus, but this will be tested to the point of death.