"Between the joists and top plate are those annoying spaces...to make my job easier"

There should not be any space. At all intersections this joint should be tightly nailed.

Sorry, explained it wrong.

Above the top plate and between joists are rectangular
spaces.

I would make a count and just cut them from the batts rather than a different product.

Foaming the rim joist spaces is now the generally accepted way of properly insulating these parts of a wall. If your budget does not allow this, at least caulk well all four edges of each space with any cheap caulking before you put in fiberglass batts. That will eliminate air infiltration through the rim joist.

While you are at it, caulk all top and bottom plates and all double studs on outside walls. The cost is minimal and goes a long way towards eliminating air infiltration.

if you are going to access these areas to caulk...
use a good caulk with a long life.
attic temps are extreme, & cheap caulks fail.

invest in a good product rather than an inferior one.

I like Dap's Alex brand 25-50 year life.

best of luck

But not in the attic, where a clear space must be left between the soffits and the top of the ceiling insulation.

Worthy makes a worthy point, make sure you're not insulating a space that is intended for air flow otherwise you'll be creating a new problem in your home. If this is the area that allows your vented soffit to create air flow to the top of your roof then your don't want to insulated this area. This is necessary for a vented roof design. You'll also create moisture issues if you cut off this air flow. That is if this is the open rectangular space that I'm thinking of..
I've steered away from using fiberglass in the walls on my last two remodel projects and have used closed cell spray on foam ( installed by a professional) instead. This especially helped in a 2x4 wall cavity that had limited space for insulation. If the closed cell foam is installed correctly, there are absolutely no gaps or air spaces. This option is very expensive but was well worth the added expense, in my opinion.
I read an article just the other day that stated just a 5% air space in an insulated area can result in a 50% air loss. Not sure how accurate this is but it makes sense if heat is constantly escaping.

"At the top of the studs is the top plate that supports the ceiling joists, or upper floor joists if you will.
Between the joists and top plate are those annoying spaces...to make my job easier I am thinking of using
low expansion foam to insulate.those spaces.
Are there any reasons why I shouldn't do it this way? "

I agree with the others, it sounds like you're describing the rim joist area. If this is DIY and you're contemplating using cans of low-expansion foam, instead consider a combination of rigid foam and canned foam.

Cut a piece of rigid foam about a half-inch smaller in each dimension than the size of the rim opening. Set the piece of rigid foam in place, then use canned foam to fill the 1/4" gap on all four sides of the piece of rigid foam.

{{!gwi}}

Leigh, you're getting great advice.

Leigh, Insulation is key for reducing costs. using the correct material in the attic can save you time, and money in the long haul. These were great advices.

Here is a link that might be useful: General contractor in Huntington Beach

A lot of good advice..appreciated.

I like the idea of rigid and canned foam.

Thanks for the replys