Here are some pictures

I hope you did not pay them yet for the incomplete install.

Why did the installers leave you with the toe kick? Why didn't they install it?

Yes it needs a backer. Do the 45° scarf joint on the skin.

Toe kicks should’ve been installed by whoever installed the cabinets...the dealer, or GC. It should not have been your responsibility.

Toe kick material is thin but the Cabinets we’ve had and the RTA ones we’ve put together had 1/2 - 3/4 plywood installed between the cabinet side panels that the thin toe kick veneer was attached to. That way you could join toe kick pieces anywhere with 45 cuts.

Whether or not it needs backing, you're gonna have some joints. You caulk it, touch it up with paint if needed and you have paint, and then you keep people from crawling on the floor. :)

I just looked at my IKEA toe kicks and they're 1/2" thick so maybe you should use 1/4" plywood to support them. I wouldn't worry about the lines. After all, they're tucked underneath the cabinets. And there are big gaps wherever appliances sit. If you were really picky you could use a line of white caulk to hide the lines between scarf joints.

Sounds like this is a DIY job...am I right? You'll need some blocking material behind toekick that thin. You have two cabinet sections longer than 8ft? Possibly you have a dishwasher or a range that interrupts it? If not, you could do some blocking material to give more to nail to.

One of my frameless lines is just like you posted.....1/4" toekick board without any structure behind it...just adjustable leveling legs. The toekick snaps to it with hardware. So this is kinda normal with some manufacturers. My other frameless line has a solid build up at the toe area...so you have something substantial there to apply it to.

@The Kitchen Place got it right, it was a DIY with help of some friend who is a professional (GC), Unfortunately he is no longer available but this is all that is left.

Anyway... I think everyone agrees I need some backing board.

Home Depot has these white plywood toe kicks (1/2" thick) for their cabinets I will use that - just to save me the trouble of handling/cutting plywood.

Then I will apply the thin pieces over it to match the color (which is kind of off white).

It is really thin but I will try the "scarf joints" anyway (I didn't know what it was called, thanks @wdccruise).

Thanks to all of you, very helpful as always.

CA glue & activator on the scarf joints will make an easier, neater job joining them.