...why we have used military power for the sole purpose of access to new markets so many times throughout history.
Fact check here. I assume by "we" you mean the USA? Then when has the US ever used military power for the sole purpose of access to new markets? Indeed, I think you'd have a pretty hard time finding instances where access to new markets was even a significant side effect.
1853, Commodore Perry brought 4 warships into Japan for the explicit purpose of forcing the Japaneses government to allow trade with the US.
Several years before his election to the presidency, William McKinley said: "We want a foreign market for our surplus products." Senator Albert Beveridge of Indiana in early 1897 declared: "American factories are making more than the American people can use; American soil is producing more than they can consume. Fate has written our policy for us; the trade of the world must and shall be ours." The Department of State explained in 1898:
It seems to be conceded that every year we shall be confronted with an increasing surplus of manufactured goods for sale in foreign markets if American operatives and artisans are to be kept employed the year around. The enlargement of foreign consumption of the products of our mills and workshops has, therefore, become a serious problem of statesmanship as well as of commerce.
Our interests in intervening in the Cuban revolution (Spanish/American war) and the Philippians (which we "won" in that war, but then they revolted against us) were primarily, if not exclusively commercial
"It is reasonably estimated that at least from $30,000,000 to $50,000,000 of American capital are invested in the plantations and in railroad, mining, and other business enterprises on the island. The volume of trade between the United States and Cuba, which in 1889 amounted to about $64,000,000, rose in 1893 to about $103,000,000." - President Grover Cleveland
"Mr. President, the times call for candor. The Philippines are ours forever. . . . And just beyond the Philippines are China's illimitable markets. We will not retreat from either. . . . We will not renounce our part in the mission of our race, trustee, under God, of the civilization of the world. . . .
The Pacific is our ocean. . . . Where shall we turn for consumers of our surplus? Geography answers the question. China is our natural customer. . . . The Philippines give us a base at the door of all the East. . . ."
- Senator Albert Beveridge
A State Department list, "Instances of the Use of United States Armed Forces Abroad 1798-1945":
1852-53 -- Argentina -- Marines were landed and maintained in Buenos Aires to protect American interests during a revolution.
1853 -- Nicaragua -- to protect American lives and interests during political disturbances.
1853-54 -- Japan -- The "Opening of Japan" and the Perry Expedition. [The State Department does not give more details, but this involved the use of warships to force Japan to open its ports to the United States]
1853-54 -- Ryukyu and Bonin Islands -- Commodore Perry on three visits before going to Japan and while waiting for a reply from Japan made a naval demonstration, landing marines twice, and secured a coaling concession from the ruler of Naha on Okinawa. He also demonstrated in the Bonin Islands. All to secure facilities for commerce.
1855 -- Uruguay -- U.S. and European naval forces landed to protect American interests during an attempted revolution in Montevideo.
1859 -- China -- For the protection of American interests in Shanghai.
1893 -- Hawaii -- Ostensibly to protect American lives and property; actually to promote a provisional government under Sanford B. Dole This action was disavowed by the United States.
1894 -- Nicaragua -- To protect American interests at Bluefields following a revolution.
"American Interests" generally means commerce, either US companies that are extracting natural resources, or else markets for American goods.
Perhaps I overreached with the absolute term "sole", but access to new markets was more than just a "side'effect", it was at times the explicit primary purpose.