Can Altcoin & Bitcoin wallets be made compatible with USDT (or any other stablecoins)? if  no, why not find ways to make any of the available stable coin compatible with the normal Cryptocurrencies Wallets?

I think a perfect Wallet should contain both a Cryptocurrency and a Stable coin pair. For example:
* Bitcoin Wallet: Bitcoin and USDT.
* Monero Wallet: Monero and USDT.
* Ethereum Wallet: Ethereum and USDT.
* Zcash Wallet: Zcash and USDT
etc..
This should enable people switch between a Cryptocurrency and its stable pair easily. The stable coin has to be thesame for other Cryptocurrencies you wish to pair with so that when you have $5 in the stable coin it will also reflect on all Crypto wallets with the stable coin.
So instead of trading on Centralized dinosaurs aka Centralized exchanges you could easily download as many Wallets as you want on your mobile phone and trade in them. A unified Widget could even be developed ( floating widgets?) for the Wallets to make Exchanging the Crypto "lightening" fast.