While I like native plants and animals, there are times and places that one will want a cleared area around the rural house. Safety from brush fires requires a cleared area for access to the house for emergency equipment and personnel. One will also want to reduce the amount of flammable vegetation within thirtyfive to fifty feet from the house. Personal, pet and livestock safety is another reason to reduce wild vegetation near the house. Poisonouse or spiny plants can result in large losses to the livestock or pet owner, and tragidy and heartbreak to the family when a family member gets injured on these plants. Wild predatory animals will tend to stay away from cleared areas in daylight. They sense their vulnerability in these open areas. If you live in an area with rattlesnakes, bears, lions or coyotes it is a fair bet to say that it is beneficial to have some clear area between the house and the brush.

If one desires to remove the vegetation from the house area one need not resort to sprays and chemicals. Nor does one need to strain ones back and muscles removing the vegetation in a fast manner. I believe in working slow and steady at something like this, but be persistent. Work at it diligently, yet with forethought and planning. Understand the lifecycle of the plants you are trying to eradicate, and work at them with a steady persistance. For large scale cactus removal I would recommend using a tractor you own or rent, or hiring a neighbor to scrape it all together with a tractor into several piles, trying to avoid killing the plants you wish to keep. This will best be done with a small tractor, not a large one.
One can also find some people who will be willing to take it down by hand. Just keep cutting the pads down and piling them up into many smaller piles. Now either way you are left with piles of cactus. These will just grow on and on if left alone. So you need to kill them all, yet not have to haul them away. Just cover them all with a foot or two of fresh horse manure. They will eventually rot (after six months to a year). But when they all are rotted down they will be great fertilizers for the soil.
After removing the tops you will still have roots that will want to regrow, you have to kill them also. You can laboriously dig them out, or take the easy way and let them rot naturally. But they will keep putting out small leaves all the time for months. Just knock them over when you see them. Eventually you will kill off all the roots by starving them. Constantly depriving them of what they need to continue growing.
Meanwhile seed the area with some native grasses. Most will not grow, but some might. As the next year goes by you will find yourself with cleared land with piles of compost scattered here and there. Next spring these could be ready sources of nutrients and humus as well as mulch material. And they will be readily accessible for use all over the area.
With this system one can do the work with less work. It just takes longer. It does not all need to be done all fast either. One can slowly expand the area worked as you go away from the house. Just make sure you keep up with the steady work afterwards of making sure no leaves grow back from either the roots, or the manure covered piles.
This method can be used to remove virtually any kind of brush from an area. Just cut it or uproot it, and pile it together. Composting or burning can reduce the volume, and perhaps result in good compost, or ashes. It is in effect a variation on the old 'slash and burn' agriculture used for millennia. It can be sustained forever if organic methods are used. The soil will actually improve year after year. Cover crops, importation of animal manures from sources where they would otherwise be concentrated resulting in high pollution levels localized in those areas. This way the manures are more spread all about. The manure will react with the brush adding nitrogen to it, and the brush will reduce the high nitrogen content of the manure. In all you wind up with clear land in a year. And almost no spines in the area after the plants are initially cut.
It is at any rate a bit of work. And it should be approached with care. Arm ones self properly with long sleeved denim shirts or good jackets, goggles and gloves. And a hand held brush cutter might be good for cutting the plants.
Take your time, avoid too much hard work at once. Use hired labor if you must. Clear the area around the house bit by bit as the years go by. Take your time, be safe.