Singlish isn't here because of any policy. It's been here since Chinese immigrants who weren't even educated in Mandarin Chinese arrived and tried to communicate with the British colonists and Malay natives.
Don't think too highly of other languages too. More than half of Japanese vocabularly are either Chinese or English loanwords, with pronunciation "modified" (i.e. corrupted) to fit into the Japanese pronunciation system to sound Japanese, and dignified with written kanji or katana in the writing system.
The problem with Singlish is that the "pioneers" were illiterate and dialect-based, mostly Hokkien. Singlish is not unique to Singapore. Malaysia, with whom Singapore shares lots of common heritage, has its Manglish too.
Mandarin Chinese is one language that's most resistant to transplanted loanwords. There are, but very few, phoenetically transliterated foreign words. The most common ones are actually "reverse-loan" Japanese-coined kanj words. But these went along quite unnoticeably as they're dignified with Chinese writing, as Japanese kanji writing is already in Chinese characters. They just fit into the Chinese language snuggly and naturally as they already have Chinese pronunciation.
The so-called "proper" English, is actually Germanic-based in grammar but overloaded with vocabulary of Latin and French origins.
There's no such thing as "pure" or "standard" languages in the world today. During empire days, the British aristocrats belittled the "corrupted" English spoken all over their various colonies, referring to them as "pidgin" English. Then English spoken in England must be "pidgin" German, right?
As the US got independent and became more powerful than Britain, the American English becomes no longer "pidgin". It became an alternative standard. So theoretically, if Singapore can become as powerful as the US, we may even see Singlish keyboard layout and Singlish spelling checker software.