What would have happened if Voldemort was sensible and made a Horcrux out of any simple object such as a stone or something and flung it anywhere?
It will be highly difficult to know the position of such a Horcrux. And no one would search for a Horcrux among the pebbles...
"What would happen"?
Nothing different - they would STILL be Horcruxes and still work. The point of having special meaningful objects as Horcruxes was all about Voldemort's psyche, not magical laws.
Harry and Dumbledore discuss this in Half-Blood Prince, with Harry having a similar idea to the pebble one you mentioned (and for a far more interesting approach, I highly recommend the famous "Harry Potter and Methods of Rationality").
However, we should not congratulate ourselves too heartily. You destroyed the diary and I the ring, but if we are right in our theory of a seven-part soul, four Horcruxes remain.'
'And they could be anything?' said Harry. 'They could be oh, in tin cans or, I dunno, empty potion bottles...'
'You are thinking of Portkeys, Harry, which must be ordinary objects, easy to overlook. But would Lord Voldemort use tin cans or old potion bottles to guard his own precious soul? You are forgetting what I have showed you. Lord Voldemort liked to collect trophies, and he preferred objects with a powerful magical history His pride, his belief in his own superiority, his determination to carve for himself a startling place in magical history; these things, suggest to me that Voldemort would have chosen his Horcruxes with some care, favouring objects worthy of the honour.'
'The diary wasn't that special.'
'The diary, as you have said yourself, was proof that he was the heir of Slytherin. I am sure that Voldemort considered it of stupendous importance.'
'So, the other Horcruxes?' said Harry. 'Do you think you know what they are, sir?'
'I can only guess,' said Dumbledore. 'For the reasons I have already given, I believe that Lord Voldemort would prefer objects that, in themselves, have a certain grandeur. I have therefore trawled back through Voldemort's past to see if I can find evidence that such artefacts have disappeared around him.'
And as you say, this would be a much more foolproof way of hiding Horcruxes than to use significant objects and then resort to a great deal of complex magic in order to conceal them from others.
DVK has already given the perfect quote from the books to show why Voldemort didn't do this, but his answer doesn't quite prove that it would have worked if not for Voldemort's desire for grandeur. It's entirely possible, from the quote given, that ordinary objects wouldn't have worked for some reason, but Voldemort never bothered to consider the possibility because of his psychological preference for significant objects.
However, JK Rowling has confirmed beyond doubt that insignificant items could also be used as Horcruxes, when she told fans that if she had a Horcrux, it would probably be a teabag:
Ewokalypse❌: @jk_rowling if you had an horcrux, what object would you use?
J.K. Rowling: I would never, ever have a Horcrux. They are evil objects created through despicable means! (Possibly a teabag).
