Personally speaking, I feel it little awkward to see anyone with a beard but no cap. It looks like there is something missing. A cap also beautifies one's outlook.
It is a part of Muslim's identity. The way a minar says this building is a Masjid, a cap says this person is a Muslim.
I remember reading a story somewhere about a group of Muslims visiting a foreign country, and the time of Jumu'ah prayer was approaching but they were unable to find any Masjid nearby. They did not know any local Muslims, so they took a car or taxi and started looking for Masjid in every lane and street. They were quite worried as the time was running short. Suddenly they saw a man wearing a topi (cap) riding a cycle. They took the car near him, said Assalamu Alaikum, and he showed them the way. He too was going towards Masjid.
They said, they would have missed their Jumuah that day if that man would have been bare headed. How on earth could they have known this is a Muslim?
There are many benefits of wearing a cap. People would say Assalamu Alaikum to you, which in itself is a good deed (10 good deeds). Someone would be in need, like wanting to know the direction of the qiblah, but they can't ask any non-Muslim, so they will be looking for any sign of a Muslim. In public places, when it is the time for prayer, when a lesser practising Muslim sees a person with a cap, going to make wudhu, preparing for prayer, then he too would feel like I should do the same. Otherwise, he will think how can I pray here, I am alone etc etc.
This is something that I have experienced myself. Whenever a Muslim prepares for prayer in a public place, and lays the prayer mat, a lot of Muslims turn up from nowhere saying I am also praying with you. 5 mins ago you wouldn't find a single Muslim there, but as soon as you start, they come out and join you. They were there all the time, but were shy to display their identity, or to start for prayer themselves.
In short, a topi always helps. Gives a feeling of belonging to Muslims, and helps supporting each other.