Well, that's not entirely true. It may not be as comprehensive as the Roman Rite or even the Anglican Rite, but much (most?) of the Evangelical denominations have their own patterns of worship, which they follow Sunday after Sunday. You may be extemporaneous in your prayer, but it's still planned and scheduled in those few minutes of singing and announcements before the lecture begins :-). Still a structure that has to be broken down and replaced by something else, albeit something with few foundations in Western culture. (At least something like the "O Come, Emmanuel" antiphon from the Roman Rite would be somewhat familiar to most coming from a Western Christian background.)
I accept your point that Evangelical denominations have "patterns of worship", but still I think it's not the same.
First of all...
Casual welcome and announcements
Stand up for 4-5 songs
During the set, or at the very end, add a short prayer
...if it's an accurate description of an Evangelical service, is sufficiently general that it could describe the Divine Liturgy in any apostolic rite. If the Evangelical in question bounces among a few different denominations, their services won't require such an adjustment as would be the case in converting to Orthodoxy or even Roman Catholicism. Moreover, even if that structure covers corporate worship, it doesn't necessarily hold true at home. When you're on your own or within a family, your personal prayer life can take any shape you want. You can follow a modified form of the church service, or some devotions out of a booklet, or something completely extemporaneous...you can even switch around among these models as you see fit.
That doesn't really work in Orthodoxy, and it only somewhat works in Roman Catholicism: in these traditions, liturgy governs even so-called private prayer. Once the Evangelical convert to Orthodoxy accepts that the rigid distinction between corporate and private prayer isn't really so rigid, once he accepts the idea of liturgical prayer, it's just a matter of getting one's feet wet, and eventually things will click.
For someone switching between liturgical traditions, however, it's a bit different. Their corporate prayer experience and their private prayer life has been rooted in a particular tradition governing what is prayed when and in what way. If you're doing it right, it becomes second nature. Its words, acts, thoughts, seasons, rhythms become a part of you, a part of your life, a part of how you interact with God and creation. If such a person converts to some other tradition, even if they are committed to their new faith, a new liturgical life can be hard to adjust to because they are expected, at least implicitly, to break old habits and learn new ones in a very personal aspect of their life: their relationship with God. As long as "old habits" are not contrary to the faith, and if they are genuinely helpful for that person's spiritual growth, I'm not convinced that they should be summarily dumped just because they aren't found in the Typikon of the Great Church. Those "old habits" could be little things or even whole rites.
Liturgy is like a language. If you have a blank slate, it's easier to pick one up than it is to grow up knowing one and then learn how to communicate as effectively in another.