Abolishing all tariffs without reciprocity Is a policy of abolishing tariffs without expecting other countries do so a sustainable economic policy? What are the arguments for or against it?

Fear of imports is very common among people. Money going out and products coming in is not a loss of anything, since products and services are just as valuable as fiat money, or any medium of exchange.

In a country with trade deficit, I should expect depreciation of the domestic currency in short term. Devaluing currency is supposed to encourage exports, and exporters but things they need for cheaper too, so it should cause some growth in exports. 

If abolishing tariffs is "such a good idea", why do politicians try to push for trade agreements instead of abolishing tariffs within their countries and benefit from the results?
You get cheaper access to inputs. For a large advanced economy that is relatively diversified, it is possible that unilateral tariff reductions across many or all sectors can be good for the economy by freeing up resources presently occupied in low-value activities with few prospects to contribute to technological progress. The additional ease of doing business in that country may also attract additional financial investments and human resources talent from abroad, which would tend to increase technological progress and productivity at the same time.

For a small economy that specializes in some specific sector (e.g., tourism, finance), a unilateral tariff reduction may improve the competitiveness of the sector they specialize in, and therefore be good for the economy and/or technological progress over both short and long time frames.

These are somewhat special conditions, and most often countries do not see benefit in unilateral tariff reductions.

As for what politicians do, this is a somewhat different question and should be considered separately from the economics argumentation about unilateral tariff reduction. It is very straightforward to argue that some concentrated interest(s) in just one or two industries could be major campaign contributors in a winning campaign, leading the politician to try to impose tariffs which benefit specific industries while causing overall negative impacts across the entire economy.

Theoretically, it would be possible to be in a situation where both a) unilateral tariff reductions could benefit the economy and b) at the same time concentrated interests could legally and/or illegally obtain political influence which resulted in an increase in their own profits at a cost to the overall economy.