I think the proposed system makes better, as the economical margin effect of working is not negligible, as it is when you just have unemployment benefits.
NB: I live in Sweden, and I'm assuming your system is similar to ours. It's a problem I have observed here and I suspect the same applies to you. I may be wrong if it works differently.
Your logic isn't backed up by places that have experimented with this.
Yes, there will always be some people who are content to live at the poverty line if they don't have to do any work for it. They are not the people to base your system around.
There are many more people who are happy to do something to improve their quality of life even a little. A problem in many countries with an advanced welfare state is that doing even a little work reduces your benefits significantly enough (and introduces so much bureaucracy into your life) that it's not work it. With a basic income, that disappears.