Why don't countries, like companies, more often merge?

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Mexico gets access to better governance

Assuming the Mexican people wanted this and that they thought the US could give it to them, how would they get it?

In this scenario, the government isn't responsive to the people so how would they get this non-responsive government to give up its power and merge with the US?

Malaysia is a merged country. I don't know of any other. Do you?

Companies by definition exist to make profit, while countries by definition do not exist for profit. It makes sense that CEO #A is willing to give up his role as a CEO for personal profit, while president/prime minister of a nation state will loose power getting nothing in return. Add to the mix all those nationalistic/patriotic/other reasons and you are in eternal status quo. I could actually add very good case study for countries not merging. Cyprus and North Cyprus, divided since 70ties, they tried to merge back together for 2 decades now. With huge economical gain for North and political for South, but Turkey does not approve the move hence, despite majority of population supporting idea it's getting nowhere. Another good case is union of Belarus and Russian Federation, despite being knitted together (economically and culturally at this stage), president of Belarus is nowhere near to accept to be another federated state of Russia (and basically being appointed by President of Russia). I would say ambition, grudges and corruption are 3 main factors while states are not willing to merge together. That being said, there are economists that claim that merges between corporations are most of the time pointless and only a device to bump short term stock valuation.

Autonomy and culture are big points. Mexicans would be losing a lot of autonomy over to the United States, and their culture would to a large degree be overwritten by the more dominant countries culture.

The only situation where I see this working is where no one country can have total power over the others. Something like the EU, if they move towards federation. But even with the relatively loose coupling the EU has, there is plenty of euroskepticism - both founded and unfounded.

In general, the advantages of mergers are not so obvious, while the costs are enormous. You can get many of the benefits of having one country through mechanisms like free trade agreements, open borders, shared currency zones etc.

When two companies merge, there is an outside institution, the government, which everybody trusts to enforce the terms of the merger and to protect the rights of the employees. When two countries merge, why would the lesser country trust the greater one to honor the terms of the merger agreement and protect its citizens' rights? There is no outside institution to enforce it. If Mexico agreed to merge with the US, and the new national government still dominated by former Americans decided to renege on some part of the deal, who would the former Mexicans go to to seek redress? There is no one, and they know that there is no one, and so it doesn't make sense for them to agree to a merger.

Because you can generally get what you want from some arrangement that falls short of complete merger. If you want economic strength without military union, you can join NAFTA, if you want military union without economic union you can join NATO. Even "mergers" usually leave their constituents as federated States with some control over their own affairs.

I haven't studied this extensively, but I'd add to drachenfels' answer that not only do leaders lack the desire to merge countries, but so do their citizens. Fundamentally, it seems that people are averse to giving up sovereignty/autonomy over the policies that govern them, and merging reduces that sovereignty.

It would be interesting to consider how the United States and EU came to be in spite of this.

Scale and Complexity? — Thinking in terms of variables and states works fine to some extent, but I think that it is always in the interactions between those variables that the states get screwed up(to a point of complete unrecognizability). And when you scale the number of variables, the interactions become too non-linear for effective management/monitoring of states. Cliched, but I feel disintegration of large is a more plausible event than coalescence of small, for with scale comes uncertainty and complexity.