Personally, I like the new menu system. I never liked the pivots, as they felt awkward.
I have very short fingers and a broad hand, so while I can hold a phone with one hand, I am unable to operate it with one hand. This even goes for using the Lumia 520, which I had for while before selling it to RumoredNow. I've always had to do 2 handed operation, which is fine with me. I'm efficient with it. I go from using my touchscreen laptop to my phone, and with these menus I am getting a better experience across both.
I know not everyone agrees. People want to do it with one hand because they are holding or doing something else with their other hand. Some people want to do it with only one hand so they can drive with the other. That I discourage heavily. When I need one or two hands free, I will use my Bluetooth headset to issue commands to Cortana for what I want done. In most cases, it's that easy. Now with full dictation everywhere you can use a keyboard in Windows 10, I don't even need to use the keyboard, or at least use it very little. Accessing the hamburger menu items is not something I do a lot. In most cases, for casual use, it isn't even necessary.
If I'm doing something more than just casual use, I'm going to be using 2 hands anyway, because it's just faster.
Besides, my carpel tunnel thanks me for using 2 hands instead of one, because using only one hand aggravates my carpel tunnel, and can lead to carpel tunnel syndrome in those that don't have it. If you've been typing and/or gaming heavily for 30+ years on various devices and you haven't gotten carpel tunnel syndrome then you are one of the lucky ones.
I'm not saying everyone should do it the way I do. It has taken me 6 months to determine that I am going to be using a device with 2 hands, no matter what size device. Because I have finally figured this out, I can now finally safely say that a larger device will suit me, whereas before I wanted to keep to a smaller size so I could use it with one hand, because everyone said that is what you're supposed to do. Well, I can't even with a small device, so why should I have to be like everyone else? If you can, great. If you can't, then perhaps you need to consider not conforming to how everyone else does it, and find a way that is more comfortable for you.
There will always be an app that you will have to reach to the top for, even without hamburger menus. If you refuse to use those apps, fine, but if it is one you really need, like your bank's app, and you don't have another choice, then you will just get used to it.
Does having to use 2 hands break up what you are doing? It depends on what you are doing. If I'm holding my 2 year old, I have to put her down in order to use the phone. That's not really cool if I need to do something on the phone while I'm trying to get her to sleep, so I understand where people are coming from.
I think moving the menu to the bottom would be a good compromise. I have to use 2 hands to swipe back and forth, because I can't reach all the way left-to-right with either hand. I would rather have the menu button on the bottom, and allow me to set a configuration option to put it either on the left or right side.