Though I am unable to answer your question of whether a legal and profitable SMS system can be built, I'd like to point out a hidden answer in your statement — "after sometime they shut the service down, something happens. I don't know why"
Most of these "ugly websites" are fly by night operators. They are spammers looking for in-use phone numbers to build a database. The database then could be used to send bulk spam SMSes or could be sold to tele-marketers for a profit. So essentially these websites never make any profit from actually sending the SMS but instead scam the users to share their phone numbers.
Most of these "ugly websites" are fly by night operators. They are spammers looking for in-use phone numbers to build a database. The database then could be used to send bulk spam SMSes or could be sold to tele-marketers for a profit. So essentially these websites never make any profit from actually sending the SMS but instead scam the users to share their phone numbers.
Now you know why!