Perhaps the reasons why churches teach mixed covenant, law & grace is because Jesus taught law & grace at the end of the old covenant. While we can benefit from them we must understand that Jesus' teachings were for a very specific 3 year period in history. Jesus was preparing Jews who were under the law for grace. The key words are "preparing" & "under the law." Grace has been here as long as we've been alive & we've never been under the law.
I dare say most churches teach Jesus like atheists would teach Jesus, as a wise historical teacher. The only difference is that Christians have "made Jesus lord" (something scripture never says to do) so they must obey Him & they think obeying Him means keeping commands He gave that scripture records. But those commands were to a very specific group of people (Jews under the law), at an even more specific time (3 year period before the resurrection), with a specific reason (to get people past sin, past the enemy, & past bad leadership to the resurrection so that they might be saved).
To teach law & grace mixed together today creates a non-reality where people work hard to receive gifts from God. That is not how gifts work! The most grace most mixed law & grace teachings give is "you get a free ticket to heaven." The truth is that people under this mixed teaching see grace as a bonus for work or an incentive to work. You get saved so you can serve God/the church.
Here's a list of things you will never see in scripture that churches teach you about salvation:
You give your life to God
You make Him Lord
You surrender to Him
You make a commitment to Him
You ask God to use you
I won't go into specific reasons why those aren't true but I will ask, "How many of those are grace?" All of them are about what you do for God. NONE, I say NONE of them are about what God did for you. Grace & the gospel are about what God did for you. All of those are works based salvation. They say YOU do the giving so God will rule over you so you can work for Him some more. 'nuff said!