Encouraging Independent Play at Home

What's wrong with playing with your son? Unless he is incapable of playing by himeself (does not sound like it), why not enjoy him? Its very important for a child to play with others, including his parents for proper development.

Humans are meant to interact with others. Your son is perfectly normal. In fact, he is acting appropriately.
Most kids are now pushed to grow up and be independent too early and as a result prefer other people or things when they grow up. Worst still, they learn to resent their parents. Parents then wonder why those kids are so distant aka independent.
You are so lucky he plays by himself before bedtime too. He sounds like he is perfectly adjusted!
My daughter is 3 and she only plays independently now and then. I see the disappointment and rejection in her eyes when I get wrapped up in a chore or project and I have learned to put those things aside. We're in the middle of moving and getting the house ready for sale. I was charged extra because I didn't pack or move certain furniture in time for the workers, etc. My husband has no time. But I just had to deal with it because time with my daughter comes first.
Nurture that trust that he has in you right now and go ahead and enjoy his affection. In a few years, he'll move on to friends, toys, TV, computers, cell phones and whatever's going to be invented. Before long, he won't have time for you. But for now, he sounds like a sweet child. You are his best friend and he prefers you over toys. That's a blessing!

I don't think you are saying that you never want to interact with your child, play, bond, ect. I was concerned with independent play when I was pregnant because my husband and I live states away from our entire family. We have no family around, no babysitters, and I knew it would be just the two of us at home, 24/7. That isn't really an issue and we have no trouble being with our daughter, playing, etc. But the reality is you do not have to constantly entertain or play with our children for all to be happy and healthy. In fact, most of us "play" with our children completely wrong, me included. There is nothing wrong with teaching or raising independent children. I read a book that said to start independent play in the crib when they are just little, before the can roll over and crawl. So I started there, I would leave her in her crib with a few toys and the radio on. I stayed close but out of sight for the most part... doing laundry, cleaning. Maybe 30 min at the most, and I would peek in and let her know I was there. Then I moved her to the floor and she began to explore her room. Doing the same, peeking in. She would play in there for about an hour. At 22 mon, she has the run of the house. If you want to encourage independent play you also have to babyproof, this will give you the confidence to walk away and let him play unsupervised for a short time. I feel confident leaving my daughter in most every room of our house alone. In the beginning start in short increments and constantly check in, let him know you are there. I would say "mommy is here, is everything alright..." or " I am just in the other room, let me know if you need me..." It might seem silly, but you are respecting them and what they need from you. Then you leave again for 5 or 10 min and so on. Sooner or later you just stop going in. Another huge point that I learned is that you have to put in the time with your child if you want them to be able to play independently. Your child has to feel fulfilled from you first. It doesn't take much, 20 min with you on the floor 2/3 times a day and the same from dad or even siblings. Twenty minutes of complete attention from you will resonate with him and fill his needs, this will give him the confidence to be alone, play alone and be comfortable and confident in his own skin. I am in school, when I do homework my daughter will play without my input or attention for a few hours. But that doesn't mean she doesn't get my attention when she needs it or asks for it. Don't think that because you want to teach your child independence that you are in any way being selfish, teaching independence early on is key and one of the most important things you can teach and foster in a child. If your child learns to play independently this gives you time to do whatever, relax, do chores, catch up on emails or phone calls, when your child sees you doing these things they learn that there is more going on in the world, more going on at home, and they are not the center of the universe ALL the time. If you want the independent play you have to also put in the time and affection (nurture) to allow independence. Alone time for a toddler is a great thing.

The toys or access to those toys has nothing to do with fostering independent play...