Well they didn't want to reform when we said we were having a referendum. Previously when other countries voted against the EU Constitution it was repackaged as the Lisbon Treaty and lo and behold didn't require votes. Now we have EU leaders saying they want to hurt the UK so much that no-one else will want to leave - despite the constituent members making very different noises.
The EU is fundamentally irreformable to reduce its power, it is the modern embodiment of Whig history - the view that progress is inevitable towards every greater liberty and enlightenment. This is the sort of attitude that leads to things like Greece being allowed to join the Euro when it was patently unready to do so.
One of the things you need to remember about the older people who tended to vote Leave is that they either voted in or remember the circumstances of the initial EU referendum in the UK. They remember what the UK joined and how it was presented to the UK. Other European countries with a much more recent history of revolution or dictatorship might want to remove power away from themselves, that is a view that is much more at odds with how Britain perceives itself.
The EU can reform, but not in the way the UK wants. The direction of the EU is towards more integration, more centralised decision making. The UK wanted less integration and more devolved decision making. There was only one viable solution in the long run.
I would not go that far as to call it undemocratic. Sure there are some deficiencies and the democratic legitimation of some political organs is clearly a bit too indirect but as you said that can be reformed (it actually had improved already over the years).
The biggest problem is that the public generally does not care much about EU law making despite the importance of the decisions made there. Only if something bad pops up the finger is pointed at the "evil EU" afterwards, ironically often by the same government which pushed that "bad" legislation forward in the first place.
The Commission operates as a cabinet government, with 28 members of the Commission (informally known as "commissioners"). There is one member per member state, but members are bound by their oath of office to represent the general interest of the EU as a whole rather than their home state.[3] One of the 28 is the Commission President (currently Jean-Claude Juncker) proposed by the European Council and elected by the European Parliament. The Council of the European Union then nominates the other 27 members of the Commission in agreement with the nominated President, and the 28 members as a single body are then subject to a vote of approval by the European Parliament. The current Commission is the Juncker Commission, which took office in late 2014.
The EU is fundamentally irreformable to reduce its power, it is the modern embodiment of Whig history - the view that progress is inevitable towards every greater liberty and enlightenment. This is the sort of attitude that leads to things like Greece being allowed to join the Euro when it was patently unready to do so.
One of the things you need to remember about the older people who tended to vote Leave is that they either voted in or remember the circumstances of the initial EU referendum in the UK. They remember what the UK joined and how it was presented to the UK. Other European countries with a much more recent history of revolution or dictatorship might want to remove power away from themselves, that is a view that is much more at odds with how Britain perceives itself.