I don't understand why you can't have all of the things you want and strict and well thought out immigration regulation.
I'm an immigrant myself, and it took us a long time to finally settle here in Canada and eventually become citizens. We had to jump through a lot of hoops to make it happen. Immigration regulations in Canada are more strict than in the U.S. I believe.. and it seems to work as a system. Canada is not overwhelmed with immigrants and the rate at which we accept them is reasonable. Some people think it's too much, some think it's not enough, but for the most part legal immigration is working out well for us here. Most complaints regarding immigration related issues here in Canada are related to all the people crossing the border illegally.
Every country has a limited set of resources and a limited number of people it can theoretically accept each year as immigrants. It would be amazing if we had unlimited resources, but we don't, so there's of course going to be practical limits as to how many people can be accepted. As such it makes perfect sense to figure out the regulations that work for your country and stick to them.
Maybe your disagreement is with the word "strict"? I'm not saying that this should imply that we only let in 5 people a year. It just means, make sure that the people being admitted are the people we want. We can only let in so many people a year, so we have no choice but to prioritize who gets let in and who doesn't. This implies strict immigration regulations, so that the whole system can function smoothly and the country doesn't end up in a position where we're taking on too many immigrants, or too little... or taking on too many immigrants who just can't figure out how to integrate into our society. It's why we mostly take on well educated legal immigrants here, as far as i know anyway. This is an investment in the future of this country, you need a solid plan for that, and you need to be strict about enforcement.