Why is there a bonus for holding honors in bridge? Isn't having 4-5 of the highest trumps privileges enough?
The rule of honors applies to any side. So if you are defending hearts holding AKQJ of hearts, you get the requisite number of points.

It really does not matter that there is a bonus for this. In the long run, the luck factor will even out: as the points go above the line.

As to why this is there: Most of initial bridge (i.e. auction bridge) terms and rules (like rubber is two games etc) and initial scoring were derived from Whist. 

Giving points for honors is no different. Doing a bit of research turns up this book on Whist: The Bridgewater treatise on Whist which details out when the honor sequences can be used to add points to your score.

In fact, I suppose some of the auction bridge rule makers felt like you did and made a rule for adding points for chicane: when you have a void in the trump suit. This seems to have been dropped from the current contract rubber bridge scoring though.

As to that making a difference, here is a story from the autobiography of Howard Schenken(Education of a Bridge Player).

Howard Schenken was playing auction bridge (note: weird scoring) and held a hand with four Aces and a Queen, when he heard his RHO bid 1NT. Without thinking, he bid 2NT and was doubled. He went down 2. So he lost 200 and gained 100 (for the honors) for a net loss of 100. He later realized that if he had just passed, he would give 10 for 1NT (remember auction bridge scoring) but gained 100 for honors for a net gain of 90! 

I also remember there was a hand (possibly in Zia's autobiography Bridge My Way) where he was given a hand (as a wager) and asked "Play or Defend". After going through all the possibilities, Zia decided to defend, getting the contract down 1. At which point the puzzle giver claimed money from Zia, because declarer has hundred honors!

In contract rubber bridge, since the honor points go above the line, they ideally should not (drastically) change the way the game is played. Though, there will definitely be a difference, I suppose.

For instance, holding xxx,AKQJT, Kxx, xx  you could potentially gamble a 3H bid over opponents 2S, get doubled, going down 1 but yet come out ahead as compared to letting them play 2S, because of the honor points.