Why there isn't a daily prayer structure like Liturgy of the Hours among Protestants?

It's a good question. Actually you mention Lutherans, Anglicans and some Methodists, which ARE Protestant denominations that do have daily Prayer/ Liturgy, so it makes me wonder why you didn't include them.

Another Protestant denomination that has daily prayer is Episcopalian.
I hope this helps explanation will help. The answer really is about the overall church governing structure. Besides the Catholic church, these other denominations are considered hierarchical, meaning that they have a supervising Synod, or governing body that determines many things from the worship style, to use of candles, responsive readings in the service as well as specific materials or curriculum for Sunday School. These are also often referred to as High Church, and this is due to the higher formality, and the clear distinction between the clergy and common people. This is by design- and we can see it in the use of the robes used by the pastor, or priest, as well as the collar.
One of the many things that are part of the history of the Protestant Reformation is that they were protesting against this over-arching structure, and rituals, which are often elevated to the point of worship/idolatry like praying the rosary.

• One of the biggest reasons most Protestant Churches don't have written prayers is that Christ spoke against vain repetition of the religious leaders.
• Another reason is that Christ gave us the Model Prayer, which is a template for how to pray, and has important elements, Adoration, confession, supplication, but it's a relationship. You don't recite written words when you talk to your spouse, and God wants us to speak from our heart.
  There are literally thousands of daily devotionals and prayer books, - but Protestants value autonomy, and there is a real danger is repeating prayers of Church Fathers, many who spread their own heresies in their writings, and this is included in these prayers. Calvin taught that infant baptism saved and it was the equivalent of circumcision.

I don't think this is a question about protestantism in general - your mention of Anglicans, Lutherans and Methodists would say that. I, as an Anglican, would count myself very much as a protestant!

The issue you mention is I think more to do with many protestant churches seeing themselves as independent or noncomformist. I myself was raised in an independent evangelical church (baptist, and then FIEC).

In those churches there is much stronger suspicion of "institutional" religion, as Nigel J outlined in his answer. In these churches, the authority of the church as an institution is downplayed in favour of a personal relationship with the Lord Jesus. This means that the church (as institution) does not exist to guide our own personal prayer life and devotion to the Lord.

Personally I think there is a lot of merit to this approach. Although I am an Anglican, and I do love liturgy, I don't use the Church of England's "Prayer during the day" in my own private devotions. I believe liturgy is only helpful inasmuch as it helps us to focus on the Bible and on Jesus.

A brief word on the question of Biblical interpretation.

The apostle Paul said:

pray in the Spirit on all occasions with all kinds of prayers and requests. (Ephesians 6:18)

We should pray all the time. Whether that be with set prayers or devotions or not, prayer should be like breathing to Christians.

I believe the Scripture passages talking about prayer are simply outlining how Bible characters have prayed at all times - there is no particular time or form of words prescribed, as Nigel J says.

As a lifelong Protestant, born into a Protestant family, then converted, personally, at the age of sixteen and a Protestant ever since, it is evident to me - if to no other - that the very nature of 'Protestantism' is a protest against, among other things, ritualistic and formal religion imposed on the individual without a decree or ordinance attached which is purely of a scriptural nature.

With regard, specifically, to prayer, Jesus never once demands prayer at specific times of day; or for specific durations ; or at any time of the week, or month or year.

Nor do any of his apostles so demand.

When the disciples ask Jesus : Lord, teach us to pray, that would have been the precise opportunity. But Jesus does not take it and says only thus :

When ye pray ... [Luke 11:2 KJV]

leaving it entirely up to the individual how they wish to organise their own private devotions. He also tells them to go into their closet, privately (Matthew 6:6) and to shut the door and to pray in secret to the Father, again making it a private matter and nobody else's business when or how or at what seasons one prays.

Also, as a Protestant, I am not required to quote 'church fathers' or 'leaders' or 'hierarchy'. I am permitted, as a lifelong Protestant, to read my own bible and to follow the words of Jesus and of his own chosen apostles.

All I am required to do, is to consent to the words of the apostles and to abide by them.

I may follow the examples of the psalmists and apostles and brethren (note well, the 'examples' - not the decrees - as is clear in the OP) but I shall not be advertising, commenting or boasting about the fact that I do so.

I shall do it quietly, in private - and before my Lord and my God.

However, if any Protestant desires advice on the matter, I would suggest the excellent homily of Martin Luther's addressed to 'Master Peter the Barber' in which Luther says (among many other things, for I recommend the entire article) :

It is a good thing to let prayer be the first business of the morning and the last at night. Guard yourself carefully against those false, deluding ideas which tell you, "Wait a little while. I will pray in an hour; first I must attend to this or that." Such thoughts get you away from prayer into other affairs which so hold your attention and involve you that nothing comes of prayer for that day.

A Simple Way to Pray by Martin Luther (written in 1535)