Is there any pressure to keep currency exchange rates around 1?

There are some counterexamples to the premise of your question:

• A USD has been on the order of 100 Japanese Yen JPY for decades. By the way, 1/100 JPY used to be called "sen", and 1/1000 JPY used to be called "rin" (source: https://en.wikipedia.org/wiki/Japanese_yen#Introduction )

Bank notes:

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• A USD has been on the order of 1000 South Korean Won for some time.

Bank notes:

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• A USD is about 3500 Colombian Pesos (COP) now. Again, it's been in the thousands for decades.

Bank notes (note that they write "mil" in small letters instead of 000):

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Note that $ denotes the peso, not U.S. dollars.

• A USD is about 20,000 Vietnamese Dong (VND). Again, it's been in the thousands for decades.

Bank notes:

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etc. These countries are not in any kind of economic crisis. The exchange rates are reasonably stable. The large numbers don't inconvenience anyone (except for some badly designed IT systems that can't handle very large or very small numbers accurately). These countries are all doing well.

Conversely, let us consider two countries at the opposite end from "doing well", whose currency is rapidly depreciating versus USD:

• A USD is somewhere around 1,000,000 Venezuelan Bolivar (VES). Venezuela did redenominate its currency from "VEB" to "VEF" to "VES", over the last few years, dropping many zeroes. It did not help. The rapidly depreciating currency is one of the symptoms of their economic problems, not the cause.

• A USD is somewhere around 100 Russian roubles (RUB). The rouble has been depreciating rapidly for years, especially after the West imposed painful sanctions to punish Russia for its aggression against Ukraine in 2014. Russia did already redenominate the rouble from "RUR" to "RUB" dropping 3 zeroes not long ago:

That did not help. Russia is still broke:

Russians looking for expired food.

Desperate Russian officials can't avert another imminent sovereign default, but are looking to delay the inevitable. They discuss redenominating their rouble again, dropping 2 more zeroes, and making 1 new rouble more valuable than 1 U.S. dollar, probably some variant of the Soviet "confiscatory redenomination" of 1947 (see https://en.wikipedia.org/wiki/Soviet_ruble#Fifth_Soviet_ruble,_1947%E2%80%931961 ). This won't help. Except for stroking Russian national pride, I fail to see the benefit of having a currency unit worth more than 1 USD.

Let us therefore look at some examples of currencies whose 1 unit is worth substantialy more than 1 USD.

• A Kuwaiti dinars (KWD) is somewhere around 3 to 3.5 USD . This does not pose any inconvenience when a subunit of the currency is small enough. A 1/1000 fraction of KWD, worth about 1/3 of US cent, is called "fil". Here is a 1/2 KWD (500 fil) bank note:

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This bottle of water costs 0.055 dinars, i.e. 55 fils, which is about 16 U.S. cents.

• Chile widely uses an inflation-adjusted currency en.wikipedia.org/wiki/Unidad_de_Fomento - 1 unit of account is worth about 40 USD. It is not available as cash (bank notes or coins), but is primarily used to denominate real estate prices, stock prices, loans, etc.

• 1 Bitcoin (XBT) is worth thousands of dollars as of this writing. Conveniently, one hundred millionth of a bitcoin is called a satoshi and can be used in transactions.

• Back when the U.S. dollar had a lot more purchasing power than it has today, prices commonly used "mill" (1/1000 USD). It's still perfectly legal (see https://en.wikipedia.org/wiki/Mill_(currency) ) and is often seen as the "9/10" on U.S. gasoline prices:

Contemporary gasoline prices.

Antique gasoline price sign: the gas costs 10.3 cents and the tax is 1.7 cents, i.e. 17 mills.

• Also the Euro (EUR), the British pound (GBP), and the Swiss franc (CHF) are all worth more than 1 USD (but usually less than 2 USD).

A good (but not quite complete) list of recent redenominations can be found in Wikipedia https://en.wikipedia.org/wiki/Redenomination#List_of_currency_redenominations . As you see, just swapping 1,000 units of the old currency for 1 unit of the new currency changes nothing. However in the 1947 Soviet confiscatory redenomination cited above, if the state owed you 10 old roubles before, then the state now owed you only 1 new rouble. But if you owed the state 10 old roubles, then you still owed 10 new roubles to the state. This may be the kind of scheme that Russian officials are contemplating again.

This is mostly done by the individual countries out of convenience. First, most countries have a main currency, say the US-Dollar, and this unit can be separated into 100 small units, ie cents. One cent is then the smallest currency unit available in the US.

So if a country had a currency with a value much higher than 1 US-Dollar, that would be inconvenient because prices could not be adjusted as accurately. Imagine everything have to cost an integer amount of US-Dollars.

Having a currency value much lower is also inconvenient because you have to keep track of all the extra zeros that don't add any additional information. This does happen as the examples Dimitri Vulis answer show. Usually prices are then marked not directly in South Korean Won but rather in units of 1000 Won again resulting in small easy to use numbers.