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At first - if you want check the requirement for visit of Italy you can check this link - this website officially connected with Italian international authorities. For Mexico it seems that you need only valid passport and you do not need the visa if your travel less than 90 days.
There is nothing about insurance and mainly I never heard about insurance check on the border for Italian non-residents. If you will apply for visa, yes, everywhere insurance is obligatory to make.
By the way I don't understand your problem. Mainly insurance for 30000 EUR of coverage should cost 20-30 EUR if you will travel for 1-2 weeks as tourist and it is not connected with extreme sports or skiing.
Moreover even finally you will find that it is not obligatory it is really highly recommeded to make - it is really your insurance that you will be paid and covered if something happen. And if you think good it is not the subject to ignore.
Anyway the absence of visa between Mexico and Italy doesn't mean you can come in the way you prefer. Border control is able to request additional information about your entrance, your plan including the information about the money you have and what for you want to live and travel during your trip, where do you want to live and do you have prepaid accommodation etc.
Also I found good idea for you: many airline websites offer travel insurance at the bottom once your transaction is almost complete - you can add to your total purchase.