The reason why there are different coin emission schemes, is that there are different ways to approach the problems of incentivizing the network and network spam. You need to somehow financially incentivize people to support the network, or the network will be weak. You need some kind of transaction fees to discourage network spam, otherwise the network will be taken down with spam.

Different coins handle coin emission in different ways:
Some coins have hard caps and intend to rely only on trading fees to incentivize the network.
Some have very modest tail emission indefinitely to incentivize the network.
Some have more sizable emission indefinitely to incentivize the network and for other purposes, i.e. funding budget system so that the project can be continually funded many years from now.

But whether or not a currency has a fixed hard cap is not the most important consideration when judging whether its economics are sound. I would consider these questions more important, and they can all be achieved (or not achieved) with the 3 models above:

1. Will the network be adequately incentivized while at the same time not cost users too much in fees?

The guarantee of a hard cap and the network being entirely incentivized by transaction fees may sound nice at first, but it can make it harder to balance incentivizing a robust and decentralized network, and having low enough fees that people will use it as a currency.

By having tail emission, you can more easily incentivize miners or stakers regardless of how much use the currency has, and allow for lower fees by subsidizing it with constant coin supply inflation - a good thing for encouraging everyday use, but possibly a bad thing for encouraging long term depending on the answer to the next question.

2. Where do the block rewards and fees go?

Some coins give block rewards and fees to miners (or split between miners and stakers), and paying miners block rewards is basically an inflation-subsidy burdened by holders who have their coin value reduced by inflation. This is when long term holding is discouraged, as long term holders can suffer multi-digit % loss in value attributable to inflation over years or decades (depending on coin).

Some coins give block rewards and fees to holders who stake (or burn fees for deflation and to prevent transaction churning for increasing fees). This is inflation-subsidy as well, but it is burdened by non-stakers, whether because they choose not to or they have insufficient balance to stake. Coins that allow anyone to stake fairly, allow all holders to counteract inflation by contributing to the network. Paying network incentive to holders themselves makes it easier to achieve a good balance between incentivizing the network and low inflation/fees.

3. If there are additional sources of coin emission, do they make sense?

Some coins are funded by donations, some by ICO, and some with built-in budget systems. Coins with built-in budget systems continually mint new coins to make sure R&D, marketing, support, etc can be funded.

Is the budget being used transparently? Cost-effectively? If not, it is possible that the budget is controlled by incompetent rent-seekers, in which case the budget is a cost that is effectively inflation-subsidized by all of the coin holders.