Hosting a dinner after private wedding?

I think it is lovely. I don't know if I would personally invite out of town guests, as I don't know if I would travel more than just a drive (no flight) for this. Nothing personal, but it is a daily short affair and no ceremony to watch. I also know someone who did this then followed up with a brewery party for 60, seemed like a great time.

Every other day I wish our extravaganza was a wee bit smaller, more on the extended family end, I want all the friends, they are the 'real' family!

It's fine to invite people to a celebration of your recent marriage. Just make sure that the invitation is clearly worded so the guests will know that you are already married, and there won't be a ceremony.

https://www.invitationconsultants.com/samplewording.aspx?p_subcategory=206

We are also doing something similar, although our ceremony will be in the same town as our "reception/celebration" but a few days before. I didn't want a lot of people at our ceremony (I'm also more private, and only want close family and friends present), but we know lots of people who want to celebrate with us, so we thought doing a small ceremony, followed by a casual bbq/party a few days later was a good compromise.

I don't think it's rude or self-centered at all! Your friends and family likely want to celebrate with you, and as long as you're clear that it's a celebration, and not a ceremony, I wouldn't think twice about it. At the end of the day, it's your wedding, and you should celebrate in a way that's most authentic to you.