Our primary reason for coming together on Sunday is to worship God - (Acts 2:47; 20:7). Our secondary reason or benefit for coming together on Sunday (if we worship the right way) is that we leave encouraged by one another - Hebrews 10:25.
The primary reason for praying for our government is so they can come to know the truth - 1 Timothy 2:4. Not just the knowledge(gnosis) of truth but the precise and correct knowledge(epignosis) of the gospel truth.
The benefit for praying for our leaders is that their knowledge of God's truth will (hopefully) open their eyes and heart to see why God's creatures should be allowed to worship God peacefully in all godliness - 1 Timothy 2:2.
There are hundreds of scriptural references that shows GOD IS WAY MORE INTERESTED IN PEOPLE (including those in authority) BECOMING SAVED than He is in any kind of freedom of worship but we are not going there for this piece. We have every reason to believe that Luke the apostle prayed for those in authority to repent while also hoping for the freedom to worship God just like the other apostles. The same Luke said that King Herod added to "all his evil" by putting John the baptist in prison (Luke 3:19-20). Imagine what Luke thought after John was killed. Try using a word like that to describe the despicable actions of those in authority today and watch the blow back especially from both Christian and evangelicals.

John the baptist was a "preacher of righteousness" who was free to speak God's truth until he spoke that same truth to power. John had the freedom and the ability to preach the word as it is written without fear or consequences. King Herod actually liked listening to John the baptist preach (Mark 6:20) but wanted John to shut his mouth when it came to speaking truth to power (Mark 6:17-18). King Herod unlawfully married his brother's wife and John rebuked the king telling him to repent. The king's wife literally wanted John's head on a platter but king Herod hated the idea of killing John. However, he gave the orders to have John beheaded (Mark 6:14-29). Jesus also preached repentance in a similar fashion to the point that King Herod thought that Jesus was John the baptist resurrected from the dead (Luke 9:7-9).
John the baptist, Jesus, Luke, Daniel, Peter, Moses, Paul etc all had strong rebukes for the government of their days. When we speak truth to power like these godly men did, it should never by mistaken as hatred, arrogance or disrespect. These godly men also prayed for everyone including those in authority but their prayer was primarily for repentance to turn to God and not a selfish desire for freedom of worship. I call it selfish because these days we want people to believe that our prayers for authorities should only or primarily be for the freedom to worship God. What's even worse is celebrating them (2 John 1:10-11) when they manipulate God's truth for selfish gains. We know better and we should be better - not perfect. When people in authority are committing despicable acts in any way, which almost all of them do, we are obligated to speak God's truth as it is written while also praying for them to come to know the truth because the truth is the only thing that can truly set us free.
Fast forward to Christianity today. You are walking down the street and see a man laying on the side of the road bleeding from the top of his head. You know he needs help and even if you can't help, you are capable of calling for help. You had the time and presence of mind to take out your cell phone, take a picture of him, post it on social media while walking away and then said to him: "I hope you feel better bro., I'll be praying for you." This sounds similar to the story of the "good Samaritan" except for the fact that they didn't have a cell phone back in the day.
We do the same thing everyday when we pray for our government without ever acting or speaking God's truth (in love) to their evil ways like John did with Herod. We are more concerned about "freedom of worship" and we look the other way even when we have the opportunity to let them know what's best for them as a human being created by God. This is not done out of love but out of loyalty that is based on affiliations. When faced with the truth about our misplaced priorities, we use excuses like "we don't expect them to be Christians" and yet, we are quick to call to repentance other human beings who are not in authority or part of our affiliation. I thought everyone was created by God and no one is above His law? I fully agree that we MUST pray for our leaders but we need to know why and what we MUST first pray for.
God brings down prideful people in authority and lifts up the humble (Luke 1:51-52) because He is not one who shows favoritism (Acts 10:34). Paul, in the second letter to Timothy, made it clear that anyone who does not face persecution in Christ is not living a godly life (2 Timothy 3:12). Freedom of worship or not, no human being gets a "free pass" to be above rebuke (in love) on their evil deeds - me included. PRAY for everyone including those in authority to repent and hopefully we will see results in the form of increased freedom of worship around the world. "BLESSED BE THE TIE THAT BINDS OUR HEARTS IN CHRISTIAN LOVE."