I prefer to do a sheet mulch to kill grass and start a new garden bed. However, sourcing enough material for sheet mulching is time consuming, and you might only be able to get enough to do a portion of the space you want, instead of the whole space.
Roto tilling isn't great for the soil microbes, but if you're starting new beds on grass that may have been chemically fried before you got the
land, and you only do it to establish beds, it can be a useful tool. Rejecting the use of a roto tiller when establishing beds can be a case of the best getting in the way of the good enough- yes, it's best if you can get enough cardboard, organic manure, organic straw, and mulch to build your beds that way, but sometimes it's not an option.
I'm having a heck of a time sourcing enough organic manure without persistent herbicides in them to build up my beds. I'd rather do deep mulch, but a shallow pass with a rototiller followed by a good mix of cover crops followed by green manure plants followed by high-quality mulch as I can get it, is going to get me to where I want to be a lot faster than insisting that everything have to be OMG PERFECT
PERMACULTURE ZOMGS! before I get anything done.
Progress is the key, don't get caught up in doing everything perfectly. If you need to till to get the beds started, just understand why it's not a good thing to till every year, and why getting away from tilling is your best option in the long run.