You are absolutely right in that it is not necessary to have an old beater for a winter bike. Your favorite all season bike will perform well enough in winter with the right tires and fenders.

However, fast road bikes do not perform well in winter conditions unless it is dry. And in winter you are more likely to crash and break something. This is not a desireable thing if you have an expensive road or mountain bike. But in the end it depends on your priorities. Some would rather just fix or maintain one bike for all seasons. Nothing technically wrong with this. Yet many bikes cannot fit the right kind of tires needed for winter. Or the right fenders and many feel better taking an old cheap beater out. In some places the salt, sand and slush raises terror with the bike drive train and many do not want thier high end drivetrain subjected to this stuff. If a mountain bike is your primary bike it can function as a winter bike better than most others. And if it's all you need or want consider yourself lucky. Some of us bike weenies need five or six bikes for different conditions to be happy.