Tonal languages seem to be limited to southern China and southeast Asia, equatorial Africa, and equatorial South America. Click languages don't seem to exist outside southern Africa. Why do these types of languages have such limited distribution? Alternatively, why did non-tonal/non-click languages spread so widely?
As a preliminary matter, "tonal language" encompasses quite a number of prosodic types, and depending on how narrowly you define "tone", you can make tone be a property with a very restricted distribution, by requiring the system to be "like Chinese" (languages that are "like Chinese" are Chinese and some adjacent languages). Otherwise, the geographical distribution of tone is very broad in the world. It is everywhere in Africa south of the Sahara: more specifically, it is lacking in Berber and Semitic. It is found in spots within Indo-European (Lithuanian, Scandinavian, Rhenish West Germanic; a number of languages of India and Pakistan), and in the European languages it is often labeled "pitch accent". It's also in Basque. Ket is the odd case of a northern Aurasian tonal language, otherwise, tone is found throughout east Asia (from India to Japan, China and south, leaving out e.g. Austronesian and some other languages). It's found in New Guinea, North America (Athabascan, Tlingit, and numerous other phyla of North America, especially in Mexico; and in various places in South America that are well north of the equator).
Clicks, on the other hand, are limited as a feature of ordinary language to a narrow region of Southern and Eastern Africa. They were borrowed into some Bantu languages, and otherwise exist in the "Khoisan" languages and Dahalo (Cushitic, adjacent to one of the northern Khoisan languages. Khoisan is not, however, a clearly established linguistic unit, and may be a set of typologically similar unrelated languages. The distribution of clicks is such that we can say that clicks are a really rare feature, but seem to be popular enough that if your neighbors have them, you might like to adopt them as well.
There are a number of sound-types that fall in the "uncommon" category, such as ejectives, implosives, breathiness and creakiness on vowels (hmmm, these have to do with laryngeal distinctions beyond just plain voicing); also uvulars, pharyngeals, and front round vowels. There is a tendency for sounds to group according to genetic phylum, which basically means that if a proto-language has a certain inventory of sound-types, daughter languages will tend to be more like that proto-language, and they don't randomly innovate masses of new sounds. Thus Austronesian languages are similar in the consonant and vowel systems, and they do not develop complex consonant systems of the type found in Caucasian languages, nor to they tend to develop tone systems. The key is "tend", so indeed there are a handful of tonal Austronesian languages, such as Yabem, Ma'ya and Matbat. Indo-Aryan languages tend not to be tonal, but there are some languages in the northern IA are that have developed tone (all, as far as I know, from earlier consonant distinctions).
My conclusion is that the geographical distribution of tone is due to the fact that tone is a less-common linguistic feature and is unlikely to just emerge from nothing. With sociolinguistic encouragement (if your neighbors speak tonally), you might dispose of some sound-structure feature (typically something about consonant phonation) and replace it with a related tonal feature. But this is unlikely in languages such as Hawaiian, Fijian, first because they don't have tonal neighbors that they may be inclined to sound like and second, because they have really simple consonant systems, and no fodder for creating tone from some other source. Tone distribution is governed by historical facts about the structure of the earlier languages, and contact facts.
Click, on the other hand, are just plain weird, and it's a mircle that any language has them.
Phonemic features which are strongly areal like the ones you mention, and a few others, such as labial-velar consonants as you see on this map, and ejective consonants. They are uncommon for some reason unknown to me. But they also spread easily from one language to another since they are easy enough to learn.
Personally, I wouldn't say that tone is that uncommon (but as you noted it is much more common in some parts of the world than others), but the reason they've turned up in Punjabi is because of transphonologisation from so-called murky consonants (aspirated voiced plosives). These are no longer aspirated, so the adjacent vowel gets a low tone. I don't personally know much about what went on in the Punjab and adjacent regions, but it is rather common for this kind of process to happen to many neighbouring languages at once. This is why we've got tone in Norwegian and in Swedish.
Clicks: although they are common in Bantu languages, apparently Proto-Bantu never had anything like a click. They were borrowed from Khoisan languages.
So click languages don't seem to exist outside southern Africa precisely because it is very rare for a language to evolve clicks. They just did once and spread like wildfire.
One theory is that climate plays an important role on developing (or suppressing) features of languages local to a region. In other words, tonal languages arise in warm and humid regions (usually, with subtropical climate).
This question (and answers to it) may shed some light: Influence of the climate and geography on the phonemes
This answer refers a work named „Climate, vocal folds, and tonal languages: Connecting the physiological and geographic dots” by Caleb Everett, Damián E. Blasi and Seán G. Roberts. Here's an excerpt (highlight mine), which is self-evident:
We summarize a number of findings in laryngology demonstrating that perturbations of phonation, including increased jitter and shimmer, are associated with desiccated ambient air.
We predict that, given the relative imprecision of vocal fold vibration in desiccated versus humid contexts, arid and cold ecologies should be less amenable, when contrasted to warm and humid ecologies, to the development of languages with phonemic tone, especially complex tone.
This prediction is supported by data from two large independently coded databases representing 3,700+ languages. Languages with complex tonality have generally not developed in very cold or otherwise desiccated climates, in accordance with the physiologically based predictions. The predicted global geographic–linguistic association is shown to operate within continents, within major language families, and across language isolates. Our results offer evidence that human sound systems are influenced by environmental factors.