Yes, the dependence on potatoes was down to the political/economic situation.
The farmers generally had a small area for growing veg for themselves. The most bang for their buck was to grow potatoes and maybe some other root vegetables like turnip or things that could be left in a the ground like cabbage. They might be able to graze a cow on commonage for milk. The milk was churned and the butter as noted above was sold for export. The liquid that was left is known as buttermilk and was eaten along with the potatoes.
Other elements - essentially all land was owned by absentee landlords, the poorer land was rented to tenant farmers as above, the better land was kept to be farmed for profit by their agents - this is where most of the exports came from. (Boycott being the most infamous agent after the famine). Other issues: rackrenting, subletting, subdivision of land, laissez-faire economic policy not wanting to interfere in markets, moralising?/judgement that it was our own fault.
Dependence on potatoes masked a lot of the problems while the population was growing as they provided sufficient nutrition.
The export of food under guard however is a hard one to get past.