given [declensions, inflections, and these sorts of things] ostensibly didn't exist at the beginning of language.

This may seem intuitive but it is not a claim that can be scientifically supported.

If this is such a strong trend

There really is no reason to think that it is. There are approximately 7000 languages in the world and they are as varied as one can imagine. While it is true that the languages you mentioned may be decreasing in sythesis there are examples of languages going the other direction.

For example, Donegan 1993 discusses the changes in two language branches of the Austroasatic language family: Mon-Khmer and Munda. They started off from the same stock and Mon-Khmer became very isolating/analytic while Munda became polysynthetic (the most extreme form of synthesis). It has not been demonstrated anywhere in the literature that either increasing or decreasing in synthesis is more or less difficult.

To make an analogy, by my understanding it's like a car on a hill. It is easy for it to roll down (decreasing syntheticness) and it takes energy to push it up.

I am sorry to say but your analogy is not at all accurate. There is no evidence to think that it is more difficult for a language to become more or less synthetic, I am afraid your view is based on a very small sample of related and geographically close languages. Many of the Native North American Languages displayed high levels of synthesis and furthermore represented a not insignificant portion of the diversity of the world's languages. Polysynthetic languages can be found in Europe (Basque), Asia, Papua New Guinea, North and South America, and Australia. I am not aware of any languages of Africa which are classified as polysynthetic (a controversial classification, but for our purposes just an extreme level of synthesis), however I know of many synthetic languages of Africa and would not be surprised to learn that there are some highly synthetic languages there as well.

Even by the most conservative estimates, humans have had language for a long time. If there was really a trend towards one morphoogical type then all languages would be like that.

If you are interested in learning more, here is short piece called Typological Distinctions in Word Formation by a well known typologist Alexandra Aikhenvald.

This is a really clear explanation from Haspelmath

I think you've got a bit mixed up, but no wonder! The process of languages becoming more synthetic, formerly called agglutination and now grammaticalisation, is widespread and much studied.

You're absolutely right that synthetic structures tend to be replaced by analytic ones. For instance many Latin tenses (perfect, future, conditional) were replaced in romance languages with analytic constructions using HABERE.

However these processes don't eradicate synthetic constructions because of grammaticalisation. The principle underlying grammaticalisations is that lexical items > functional (grammatical) items > morphology > morphophonemics > zero. So if you look at what happens to HABERE once it's incorporated into romance languages, in some cases it ends up forming a tense inflection, completely losing it's meaning of 'to have' and creating a new synthetic future tense: CANTARE HABERE (VL) > cantar he (OSp) > cantaré (MSp)

I hope that makes sense!

That's not a universal trend. It's not unlikely to picture a future English where prepositions are not treated as individual words but merely part of the words they modify, and pronouns part of the verbs e.g. "I go to the store for cheese" turning into "I.go to.store for.cheese". And then imagine a little later on, there are phonetic changes such as dropping of the "r" in "for" before consonant clusters, rendering "Igo tostore focheese and forapples" or in second person "yougo...".

You would thus be very well on the way to a synthetic case language with different declensions as well as regular conjugation of verbs. The analytic systems of Proto Indo-European may have originated in precisely the same way, i.e. via post-positional particle systems, cf. Japanese. Japanese, actually, used to be far more analytic than it is today.

Increasing the number of morphemes per word can easily be achieved by grammaticalization where things like e.g. pronouns or auxiliaries are turned into suffixes.

I can't tell you anything about the current stage of every language in the world; the ones you're mentioning are part of the European sprachbund and their similar development is likely due to mutual influence.

EDIT: Here is an example from Romance taken from Campbell 1998

So we start off with a periphrastic construction (in Vulgar Latin, I presume) for the future tense and end up with a tense marking suffix on the verb:

cantar he > cantar-hé > cantaré 'I will sing' (he 'first person singular' of haber) cantar has> cantar-has > cantarás 'you will sing' (has 'second person singular' of haber)

The Unfolding of Language by Guy Deutscher is about this topic. Basically, the process is like a circle. Languages build things up and then pieces erode away.

Essentially, words are "absorbed" into other words to create new inflections. An example is English's "I am going to..." which in common speech has observed a high level of contraction such that it simply becomes "I'm'a." People don't tend to think of this as a language "gaining complexity" - and in fact often decry it as "degeneration" of language - but this is precisely how languages gained their inflectional complexities in the first place. In the example I gave, English's extensive use of contractions with pronouns and modal verbs may well give rise, millennia hence, to a system of "pronoun conjugation" as seen in Wolof of Senegal.

Another example is in the Romance languages. Classical Latin had its own future tense, but more usual in Vulgar Latin (the language of the common Roman folk) was the use of a compound tense with "infinitive + habere." Parabulare habeo, for instance, meant "I will talk" (not "I have to talk," though the construction is analogous). This carried over when Vulgar Latin developed into the modern Romance languages. In Spanish, "I will talk" is hablaré, a contraction of hablar + he, where he is the first person singular present form of haber. The haber portion of the analytic compound tense "fused" into the infinitive to create a new inflectional, synthetic form.

A third example is from Hungarian. Modern Hungarian has an extensive case system - 18 cases, most of which correspond to various prepositions in English. Indeed, just a thousand years ago, these were postpositions - essentially prepositions placed after the word. But the rapid pace of human speech caused these words to fuse into the nouns they modified, and they became suffixes.

There are countless examples, but this is the essential process that occurs.