What are the cons if we allow browsing of cron.php?
The main argument against it are the limitations of webserver requests. The circumstances where you cant run a cron via cronjob/cli, usually also involve strong limitations on memory consumption and max script run time.
So running it from there is likely leading to cronjobs being only executed half because they hit the memory limit, or they are just running to long.
Another reason is, that it blocks your webserver with a long running request. On cheap hosting plattforms this is one of the behaviours, which leads to get thrown out of the hosting.
For Magento 1.9.x, I think
SUPEE-6788 (security patch) forbids calling the cron manually from the browser by default. You would have to update permissions and/or change
.htaccess before calling the example.com/cron.php URL manually from the browser.
Try running this from the command line:
php /path/to/magento/cron.php -mdefault
If that doesn't work, see here: After applying SUPEE-6788 , cron stopped working
Disclaimer: I haven't worked with Magento
1.9.x much recently, more with Magento