I think you can buy an electric powered edger, to use on your flower beds, or wherever ya need to trim the edges. I just sharpened the blade on a really ancient Craftsman edger, this past week.

Think about it. If the cutting blade were wider than the wheel-base how would you prevent the blade from hitting the wheels? The offset-wheel Lawnboy-design comes closest to what you are describing.

I have two string trimmers, but my objective is to not need them. I want the mower to trim the edges. Most ride-on mowers do this because the cutting blade extends a few inches to the right of the wheels. I don't want to buy a ride-on mower, just a regular mower.
I would like to find a non-riding mower build this way. The wheels would need to be extended forward and rear and made narrower so that the cutting blade would cut to the left and right of the wheel base. Not a big deal, and a very useful mower. Why doesn't someone build a mower like this?

I'm not sure such an animal exists. There are several wheel edgers designed for "curb hopping" with an adjustable rear wheel which can be lowered as much as six inches relative to the others. Sears and MTD both make such machines.

You don't say what the relative height difference is between your flower beds and the height of the lawn.

If we are talking 2" or less, you might get by with a mower that has the four wheels independently adjustable. You'd set the left side as high as possible and the right side to the correct cutting height. If the difference in wheel settings were the same as the difference from grass to flower bed, you would ride level while dropping left side wheels into the flower bed.

I was going to suggest Snapper (I use them) as they have separate adjusters. However they have a solid axle connecting the wheels from side to side, making the adjustment impractical. Perhaps a cheaper mower with each wheel connected to it's own axle stub would give you the articulation you want.

I guess I was wrong. I can now picture a mower with an extremely long wheel-base and a blade that spins between the wheels. Don't know anyone that makes such an animal though.

Just like what "evdpgh" says, the old 2 cycle lawn boys with the off set wheels cut wider than the wheels.

I second the recommendation for the stagger-wheel Lawnboy models. You still have to use a weed trimmer for very tight spots, though.

I am also looking for a lawn mover that cuts wide, so I don't have to use a trimmer. Anyone found one that cuts beyond its wheels? Can't believe that they don't manufacture such a mower...

No - but an affordable option is a large deck - 21” is the standard now but you can go up to 30”. The bigger the deck the easier it is... I just replaced my 19” Battery Powered with a 21” Gas mower, it’s definitely easier around trees, flower beds and slopes, I have a couple spots that are tricky to mow

I have a 20'' battery powered and it worked nice in the beginnings, but now the battery doesn't last I keep getting replacement 40v batteries that overheat in texas heat, so it takes stopping and changing batteries 4 times. My yard isn't too big, but it is not small. I guess about 6000SF of grass. I will keep asking for replacement batteries until the warranty expires, but after that I think I should invest into a nice gas one. Based on these comments I looked up toro, and there is nice 30'' one but it's $999. If I can be sure that it gets very close to garden beds edges I would make the investment. We just planted new trees and new garden beds and more flower beds and now I have over 300feet of edges that I have to go around with the string trimmer and it just too much work... Why can't there be just a lawn mower that has the wheels extended forward and rear and made narrower so that the cutting blade would cut to the left and right of the wheel base basically almost touching the flower bed edging....

Interesting, I have the same experience with Battery Powered mowers, finally bought a gas mower. One thing that might help is the castor wheels at the front like this Cub Cadet model, again high price point but ideal to get a precise cut around flower beds etc

https://www.cubcadet.com/en_US/wide-area-mowers/cc-600/12ACW6M9710.html

https://youtu.be/zs0HBHM7FFE

If you’re interested in the Toro Timemaster this one’s a good review - to me it seems like the deck is a bit wider than the wheels

https://youtu.be/f60dDi0zAGg

A good channel to follow if you like Toro

I don't have a brand preference, I just bought my first mower with my first house and first yard. If I find one that the deck is wider than wheels that would be my preference. The other alternative are these plastic edgers that supposedly eliminate the need for edging after mowing. But i am not sure about this concept and look. https://www.homedepot.com/p/Emsco-20-ft-Bedrocks-TrimFree-Resin-Slate-Lawn-Edging-2032HD/100640930

That seems like a good option to me, you could go with a more affordable option for the mower and you likely don’t need to purchase a string trimmer. You could also look at manual tools for edging and weeds.

String trimmers can also be used as edgers and there are 4-cycle gas string trimmers now