(1/2) Funny you should ask this question today, on the 187th anniversary of the illegitimate occupation of the Malvinas Islands (Falklands) by the British on January 3rd 1833, islands that were then part of Argentinian territory. This was one of the key moments in history when the Monroe Doctrine did not apply.

Couldn’t it also be interpreted as the US seeking to protect the newly independent Latin American republics from recolonization by European powers?

The main problem with this interpretation is not the core theme, the protection of other countries from recolonization, but rather, the reasoning behind that protection. If we were to judge foreign policy from an idealist perspective, sure, one could imagine that Monroe may have wanted to shield the continent out of pure kindness. However, it would be important to note something about the Monroe Doctrine. Most quick google searches will give you an abridged version of the full text. Heck, the wikipedia page explicitly says:

The full document of the Monroe Doctrine, written chiefly by future-President and then-Secretary of State John Quincy Adams, is long and couched in diplomatic language, but its essence is expressed in two key passages.

No, it's not just expressed in two key passages. A more thorough analysis of that six pages "long" speech, riddled with "diplomatic language" (which, granted, talks about many more things than just the Doctrine) can allow us to understand that, from a public foreign policy perspective, Adams and Monroe's intended to "protect" the continent, when and if it suited the US' interests. The first of those mentioned passages states that:

(...) In the discussions to which this interest has given rise and in the arrangements by which they may terminate the occasion has been judged proper for asserting, as a principle in which the rights and interests of the United States are involved, that the American continents, by the free and independent condition which they have assumed and maintain, are henceforth not to be considered as subjects for future colonization by any European powers. (...)

The highlighted part already shows what I mean, because it clearly states that such consideration stems from the US' rights and interests.

(...) We owe it, therefore, to candor and to the amicable relations existing between the United States and those powers to declare that we should consider any attempt on their part to extend their system to any portion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependencies of any European power we have not interfered and shall not interfere, but with the Governments who have declared their independence and maintained it, and whose independence we have, on great consideration and on just principles, acknowledged, we could not view any interposition for the purpose of oppressing them, or controlling in any other manner their destiny, by any European power in any other light than as the manifestation of an unfriendly disposition toward the United States. (...)

(...) It is impossible that the allied powers should extend their political system to any portion of either continent without endangering our peace and happiness; nor can anyone believe that our southern brethren, if left to themselves, would adopt it of their own accord. It is equally impossible, therefore, that we should behold such interposition in any form with indifference. (...)

I can understand why the doctrine may read as a wholesome ideal of protecting other nations’ right of self determination. However, it should be noted that, throughout the years, the doctrine was applied only when it suited the US government’s interests to do so. The protection of Latin American nations and the entirety of América as a continent, was relegated to a secondary position, when protecting a specific country conflicted with what the US government needed from the European country at fault.

Starting in 1833 with the aforementioned British occupation of the Malvinas Islands, came a long list of instances in which the US turned a blind eye to European imperialism in América. Some of the most prominent examples were the Anglo-French naval blockade of the Argentinian Paraná and De La Plata rivers, of which I spoke about here; and the French invasion of México and the subsequent imposition of Maximilian as Emperor of the Second Mexican empire. More recently, the US refused to help Argentina during the Malvinas War of 1982, siding instead with Thatcher’s government, providing the English armed forces with intelligence on Argentine forces.