what are the pros and cons (if any) for putting mulch on the top of potted figs the shredded bark mulch  called landscape mulch, about an inch thick.i remember reading that as the mulch breaks down it draws nitogen from the soil, is this true or old wifes tale? thanks

Pro for me: Helps keep the moisture,keeps the soil in and cuts down on the grass.

From what I have read nebo, that is true for hardwood mulch. And less so for pine bark mulch. Best to us pine bark, but still fertilize.

when bark mulch is mixed with the soil, it will draw N when rotting.
when on top, there isn't enow interaction to allow that.
the benefits strongly out weigh the drawbacks of eventually mixing it in.

I use about 4 to 6 inches of bark mulch around my trees. Really holds the moisture well. I figure if it's on top, it's not drawing much nitro. In addition instead of composting, I throw leaves or any other small plant debris and sweepings into my fig tree circles as well. I wouldn't do that with my other fruit tree's, as I've read that it can have a girdling effect destroying bark and killing the tree's after a number of years, but it hasn't bothered the figs at all. The worms and sow bugs and other continually work at the bottom of it turning it to soil after a few years. I think it's very beneficial.

It helps reduce watering

I use pine bark mulch on my potted trees. Main reason is it was cheap.
Lowe's had damaged bags for $1.00. I bought ten bags and used some around my raised garden beds.

Pros - it helps pots from drying out on hot sunny days
Also hardwood mulch seems to decompose a lot faster than pinebark.

Cons - none

I use pine bark, keeps in moisture, doesn't rot as fast.

In my experience if the soil is very rich, the mulch does not affect at all. on the contrary it helps to maintain humidity and stops weeds from growing.

I wish I would have taken pictures from last year to show you guys, but what I found was that under the mulch, I had roots growing all over the soil surface as well as under the soil.  I consider that a good thing, especially on varieties notoriously not vigorous such as Black Madeira.  I never had problems with mulch strictly being used as mulch should be used on top of the mix rather than as an amendment.  Never mix it in.