The statistics given for the different wars aren't the same. In particular, the deaths listed for most of the early wars are the "killed in action" and "died of wounds" deaths, while the Mexican-American War and the Civil War death totals given include other military deaths. By far the largest part of this other number for the 19th century and earlier wars is deaths from disease.

For example, the Civil War total Union dead of about 360,000 includes about 110,000 battle deaths, about 220,000 other deaths, mostly from disease, and about another 30,000 deaths in prisoner of war camps. The Mexican-American War includes over 11,000 disease deaths. The WW1 deaths include about 63,000 other deaths in addition to about 53,000 battle deaths.

If we add other deaths to, for example, the War of 1812 (possibly about 10,000) and the Spanish-American War (about 2,000), the total deaths exceed the wounded.

The wounded statistics aren't the same in all cases, either, as some count the number of individuals wounded, and others the number of wounded cases which will double-count those wounded multiple times, and also count those later killed (or died of disease).

For a convenient database listing other deaths for the Civil War onwards, see https://dcas.dmdc.osd.mil/dcas/pages/report_principal_wars.xhtml