Any wood that contacts the ground needs to be treated against insects. That does not mean it will last forever. The only reason I can see why pavers laid over timber might cause damage is that water filtering between the stones would not dry out, and that would attract insects even on treated wood. Should the base under pavers settle, those half on/half off the timber edge could crack when walked on.

There's an area of my yard with poor drainage.

I am really not understanding. Presumably any hardscape (pavers) will be nearer the house. There should be no water issues near the house, or there will be bigger problems. Pavers will not alleviate water problems. Raising the pavers will not alleviate water problems, but might even exacerbate them. Using wood as an edging for pavers is a poor decision. You should be using paver edging, plastic is common, aluminum is available. I might be questioning your contractor's ability to install the project correctly, they should review Techo bloc installation instructions and details. The drainage should be considered separate and dealt with.

To maintain the budget...proposed wood border. You might pay less now using wood, but in the long run when you have to replace rotted wood, etc, you’ll end up paying much more than what you saved.

What is the cost of wood border saving compared to what anyway? More info please.

@3onthetree - I apologize for any confusion. The pavers aren't intended to solve the drainage issue on their own. A separate drainage system will be installed in the area as well. My understanding is that by replacing the dirt/grass with pavers, it'll be easier to direct the water toward the newly installed drainage pipes. Please let me know if you disagree.

The alternative that I was offered was to dig a trench along the edge where the pavers will be installed, pour a concrete base, and use cylinder blocks. I'm told that this would nearly eliminate any future problems with the pavers (or at least eliminate any problems within my lifetime). Also, with the cyliner blocks, my understanding is that it'd be possible to put stone edgers on them if desired. The difference in cost is about $4K. We've already poured in about $30K so far (includes the installation of the pavers and drainage system, replacing and widening a concrete driveway, and construction of a playground area with leveling of a portion of the yard - which worsened the drainage issue and requiring the installation of the pavers, etc.).

Yes, I would disagree about using pavers to direct water to drainage pipes or using them to solve some sort of water problem. Any hardscape, even solid pavers whose joints allow some absorption of water to below, will cause a more concentrated load of water runoff to whereever it is heading. Grass areas will absorb much more water, and once the soil is saturated any additional sheetflow (surface water) can be directed somewhere via swales (shallow broad "ditches"). I am not sure what your description of concrete block or stone edging on the paver areas has anything to do with drainage, unless you are making irrigation ditches for California crops. Drainage is solved via grade elevations, swales, and if need be french drains. Problems near the house are solved with slopes away from, downspout leaders, or again french drains if desperate.

Pavers are installed with sand. Although sand drains quickly overall, the tiny aggregrates will retain enough moisture where sitting against any wood leads to accelerated rot.

Much information is missing, but from the sounds of it so far, your contractor is making lots of money and you keep throwing more money at it (whatever the original problem was) that may not be helping.

No wood edging for me. I built our patio 20 years ago. It has been extended into the drainage swale from home construction.

To deal with the water, after excavating the top soil i trenched a French Drain around 2 feet below grade. The trench goes all-around the patio perimeter and empties where the swale goes between homes. My paver block edging goes 16” below grade resting on compacted crushed rock. The pavers are set in limestone screenings atop 12” of compacted crushed stone. Only minimal movement has ever occurred and I reside in northern IL where the frost can go 36”. Hope this helps.