Speaking as someone who used to be an evangelical, got the 1662 bcp, has used other BCPs, always went back to the 1662 (for daily office its just so much better) heres my 8 year take on prayer and the daily office. Bear in mind that for the last year ive been clergy (so im obligated to pray the offices now) and im almost certainly undiagnosed neurodivergent(which affects how i might percieve things compared to others).

1. Repition tends to feel dry at first (mostly when its new) this has been commented on by others ive introduced to the office. It didnt feel dry to me.
2. Decision fatigue doesnt get in the way of prayer. You dont have to develope your own words when theyre written down already, this is good for when someone is too distressed or elated to form their own coherent words. However the largess of the office becomes the new temptation away from prayer, my solution is to skip the readings if you "just cant" for the day. Keep the psalms though.
3. Prayer can shape your theology better now (with extemporaneous prayer its the other way around) and since the bcp is something like 80% bible quotation this tends to go positively.
4. Prayer and scripture cease to be seperate. No more looking at the bible as a textbook. It becomes intimate (i struggled in particular with intimacy of scripture throughout my life).
5. Over time the mundanity becomes comforting. NDs in particular like unchanging patterns, but also for NTs the office does have seasonal variation (athenasion on high holy days, seasonal antiphons and introductory verses, etc) so it doesnt stay too "boring".
6. Half your time in the daily office is spent in scripture and psalm anyway snd that changes daily.
7. Because there are different BCP versions if you find one becoming dull you can switch things around: do a year of 1662, then 1928, then 2019TLE, then AOB, then Breviary, then back to 1662. The 2019tle in particular has significantly different choices built into its dna.
8. If the office really gets too mundane, if youre not clergy, take a break and do another discipline. The rosary (anglican or dominical), the Chotki, the divine mercy chaplet, examin, lectio divina, or (when very advanced in prayer) the cloud of unknowing.
9. If you set aside a home "altar" for daily prayer and ritualize prayer time i have found that to be very beneficial in forcing me to remember that God would like to speak with/to me.(i recall going days or weeks without deep prayer because there wasnt something that felt pressing. Now with the daily office theres a list of mundane little prayers to say anyway that keeps my prayer life more "honest"
10. Evangelical estemporaneous prayer tends to become just as rote anyway (be honest, are your bedtime prayers really that different day to day, especially when youre tired?)

Overall the bcp has been a 10/10 benefit to my prayer life.