I like burn more than none, just for the fact it's faster.
If you say it's not faster, because you could wipe and get sent to orbit to start over, that's because you and/or your fireteam are terrible.
I, and tons of others, solo Nightfalls on a regular basis with no problems. It's also great to drop high-hp enemies that deal heavy damage (Colossus, for example) in a much faster time.
And for OP, the weeklies usually don't have a burn modifier. It [i]is[/i] nice to have, though.
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^ this Solo these as well. Valus is going to take forever. Pack a lunch.