Yes, many would see the visa-free travel to the EU as an important thing, and the key words here are: reputation, acknowledgement, and recognition.
The EU officials make a clear link between the Ukraine's elimination the corruption and organized crime and, on the other hand, receiving the visa-free travel.
Visa-free travel is often perceived as an ability to hand your passport to the Immigration officer on the border and get your entry permit.
But inside, the process is much more complicated.
During maybe one minute, the officer must get enough information about the traveler: their criminal record, for example.
When you apply for the visa normally, a Consulate does essentially the same, but they have dramatically more time than an officer at the border check.
So, visa-free essentially means that a country X trusts the country Y:
- integration of the databases between the countries;
- sharing the criminal and financial records and other similar data;
- recognition that these data are not forged;
- effective prosecution of people who are accused in corruption, organized crime, etc.;
- acknowledgement, formally declared in international agreements, plus hundreds of smaller technical regulations;
Look at Ukraine before the Revolution of Dignity (2014). It was widely recognized as a semi-colony of Russia. Albeit formally we were an independent state, the whole country was under significant influence of Russia:
Ukrainians came to streets and squares to not only overthrow the pro-Russian regime, but also to start building normal relations with the developed world, and, most importantly, with the European Union as our closest neighbor.
- we started eliminating corruption and tackling the international organized crime;
- we are cleaning our government from enemy's agents;
- we are rebuilding our security services to make it closer to the standards of NATO;
- we successfully withstand the foreign armed invasion;
- we adjust our technology and quality standards to make it closer to the EU ones; this seems to be a huge step toward liberalization of the Ukraine-EU trade and, hopefully, signing at some moment a free trade agreement, like this one;
The last three years have seen the birth of a new Ukraine, that advances its democracy and economy through sometimes very tough reforms.
Additional assistance from Europe should help Ukraine in strengthening its democratic path.
— European Council President Donald Tusk (BBC.com)
The EU officials make a clear connection between the fighting corruption and receiving the visa-free travel. Quoting the same article:
The other major matter on the agenda at Thursday's meeting was corruption, and the country's record on tackling it came under scrutiny.
EU officials have been urging Ukraine since 2014 to clamp down on corruption and to carry out other reforms. But critics say not enough has changed, and Mr. Poroshenko has been accused of backing corrupt officials.
I do not claim that Ukraine has already eliminated our "colonial past". It took merely 25 years of hard work for other countries who were in a similar situation: Poland, Latvia, Lithuania, and Estonia, to name a few.
Realizing that the recognition must be earned, Ukrainian people are slowly but surely changing their country, and struggling for the EU to offer the visa-free as one step forward to the full Euro-integration.
Fighting the Euro-Skepticism
Also, the visa-free travel seems to be an useful thing for the EU, too. During the recent years, the EU suffers from euro-skepticism. The enemy's propaganda is working hard to undermine the EU's integrity. This ended up with brexit and other destructive processes with the Union.
Realizing that some countries are trying their best toward Euro-integration is arguably a huge factor for raising the morale within the Europe itself.
That's why the visa-free travel is a big deal for both Ukraine and the EU.