Old Testament quotation in Rom 10:5

Rom 10:5-15 has a number of interesting quotes of the Old Testament.

I am struggling to figure out exactly what Paul intends with these quotes.

The first quote is an indirect quote Moses from Levitcus. Paul wrote:

Rom 10:5 For Moses writes that the man who practices the righteousness which is based on law shall live by that righteousness.

This is a quote of Lev 18:5:

Lev 18:5 'So you shall keep My statutes and My judgments, by which a man may live if he does them; I am the LORD.

The fact of the matter was that Israel had failed to live up to the statutes and judgements. By the time of Ezekiel this was quite plain.

Eze 20:21 "But the children rebelled against Me; they did not walk in My statutes, nor were they careful to observe My ordinances, by which, if a man observes them, he will live; they profaned My sabbaths. So I resolved to pour out My wrath on them, to accomplish My anger against them in the wilderness.

This quotation seems pretty straightforward. It does seem also to match the sense in which Moses wrote it. If a person lives by the statutes and judgements they will live. Was the mistake that the Jews made to assume that live meant be deemed righteous? Moses does not make that statement there.