I have only had one coached pushing and it was with my epidural. But even then it was the biggest joke because I was the one that told the nurse i felt like i needed to poop (30 minutes after they had checked me at a 2) and she told me it wasn't possible and to just poop since it would be taken care of later. Thankfully i was very adamant that she check me and watched in glee as she hurried around getting everything ready and calling the doctor since baby was RIGHT there. Now when having an epidural, yeah it can be semi helpful as you don't feel everything. But your body still does what it needs to do and 28 minutes later dd was out (she was my first).
Now my 3 unmedicated home births, if anyone had dared to count to 10 while i pushed i probably would have kicked them out lol. Really a contraction doesn't always last 10 seconds. And if it's only lasting 10 seconds . . .it's not going to be a very useful contractions and quite frankly, you shouldnt be pushing yet. With dd#2 i decided that i wouldnt flinch a muscle till i couldnt do anything else. 1 push and 30 seconds later, she came flying into my dh's hands (mws had gone into another room). There was no need for coaching or cheerleading (as i call it). DD was born posterior with a nuchal hand no less. With the last 2 births, again, no need to be coached. With the very last birth my mw's didn't even know how dilated I was when i started naturally pushing and it was more of a i need to grunt and crouch and bend and move my body this way and that, and then oh wow I need to get on hands and knees and move this baby OUT, sort of thing.
Now in more trying labors, when mom has been pushing for hours and she's exhausted, baby is exhausted and it feels as if she's at the end of her rope. . . this could be a good thing. As long as the coaches are willing to listen to the mom and not count (again who ever set contractions to being as long as to the count of 10?). But more along the lines of positive affirmations and letting her know she is amazing, she is beautiful that she is doing it right and to keep pushing and to listen to her baby.
Trust your gut on this. Our mothers come from a different era of birthing so sometimes they don't understand our 'new fangled' ideas of birth lol. But you will not lead yourself wrong. Happy birthing!