I've create this answer after referring above all comments & answers. This will resolve the dropdown population error even it get disabled.
Step 01
Html.DropDownList("Types", Model.Types, new {@readonly="readonly"})
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Step 02 This is css pointerevent remove code.
<style type="text/css">_x000D_
#Types {_x000D_
pointer-events:none;_x000D_
}_x000D_
</style>
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Tested & Proven