Pros & Cons of Buying an Integrated with Built-in DAC?

Buy the best 2 channel integrated that's in your budget without a phono stage or DAC. You'll always be better off buying an outboard phono and DAC than a Swiss Army Integrate. Look for something used like an Ayre, Pass or ARC and you'll be happy. 

+1 adg101. Purchase a separate DAC when needed. There always is a number of quality used DACs on the market when one is interested. 

An integrated amp with a built-in D/A is the modern equivalent of a receiver and all the old pluses and minuses apply.  It's a single box as opposed to multiple boxes and requires only a single shelf space.  You don't need interconnects (or additional power cords).  No need to fret over mismatched gain or impedance matching.  A single remote control.  The downside is you can get better quality (at a higher price) with separate components.

Newer D/As will decode higher sampling rates of both PCM and DSD.  If you are downloading these hi-rez files, then get a recent model converter.  My experience is unless you go above $3k all D/As more or less sound the same, which is uniformly good.  My question to the OP is "do you have a reason not to go with an integrated solution?"

If there's no demand on higher power, the combination units similar to vintage receivers will work great depending on unit quality.
Many vintage receivers tuner/preamp/amp combos compete very well against modern full function integrated amps

I agree with ADG - get the best sounding integrated amp you can, and then add a separate DAC.

I've been using a Meridian 263, from about 1992, and it is still very good musically/sonically.  The downside is that it won't work with any newer formats, but since it was effectively free I don't really care. 

Good, inexpensive DACs are all around these days.  Don't limit yourself by trying to put everything in one box unless you really have to.