You mean like this: ÷ ??
Historical reasons.
Computer keyboards are based closely on the old typewriter keyboards. With the old mechanical typewriters, every additional key and keybar added cost, so they had as few as possible. Up until the 60s or so they did not even have digits one and zero - you used lower case L and upper case O, respectively. Very few typists ever needed a division sign, but the slash (/) was recognized as an equivalent, and had lots of other uses too, so the / got put on the keyboard and division did not.
If you really wanted a divide sign you could fake it by overstriking colon (:) and hyphen (-). The exclamation point was similarly done by overstriking the single quote (') and the period. I'm not kidding.
IBM eventually introduced the modern typewriter layout, very close to the current standard computer layout, first with the IBM "Executive" proportional spacing typewriter, and then with the Selectric. One and lower case L are different widths, and so are zero and upper case O, so the Executive really needed those digit keys and the Selectric line followed suit. These machines had 44 printing keys (not counting space, backspace, return, etc.). Still the division sign was not important enough to include, although of course Selectric users could pop on a special "Symbol" typeball if they really needed to.
As computers were developed alongside these machines, they largely copied the typewriter keyboard layout. When the first computer languages (like Fortran) were developed in which you could type reasonably arithmetic-like formulas, asterisk (*) got used for multiply and slash (/) for divide. Computers in those days typically used only 6 bits per character and only had about 48 different characters (including space!) they could print, or that could be input via punched cards, so there wasn't room for new special characters when existing ones could be made to do double duty.
(I know: six bits would mean 64 different characters. But the printers only could print 48 different ones. The more different characters were on the print train or chain, the slower the printer ran, so it was advantageous to keep the printable character set small.)
Heck, even plus, equals and the left and right parens were not always present. The 48-character printers and keypunches had two different printing character sets, the "scientific" set which did have the + = ( ), and the "commercial" set, which had & # % and a weird thing called a lozenge instead. Square and curly brackets? Less than and greater than signs? Forget about it.
And the slash-for-divide convention has stuck ever since. The "divide" sign wasn't in the seven-bit ASCII code either (which had 94 printable characters plus the space).
But if you really want a divide sign today, it's in most code pages. You can get it on Windows with Alt-0247. (Hold down the Alt key and type those digits on the numeric pad.)
The multiply sign, Alt-0215, is also available. It is not really the same as the letter x:
using the multiply sign: a × b = ab
using the letter x: a x b = ab
the difference is much more noticeable in "serif" fonts. But even in sans serif, the multiply sign is clearly not "just another letter" as the x appears to be.